Discrete Mathematics With Applications
5th Edition
ISBN: 9781337694193
Author: EPP, Susanna S.
Publisher: Cengage Learning,
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Chapter 9.9, Problem 21ES
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To explain what must be true in order for
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Assume {u1, U2, u3, u4} does not span R³.
Select the best statement.
A. {u1, U2, u3} spans R³ if u̸4 is a linear combination of other vectors in the set.
B. We do not have sufficient information to determine whether {u₁, u2, u3} spans R³.
C. {U1, U2, u3} spans R³ if u̸4 is a scalar multiple of another vector in the set.
D. {u1, U2, u3} cannot span R³.
E. {U1, U2, u3} spans R³ if u̸4 is the zero vector.
F. none of the above
Select the best statement.
A. If a set of vectors includes the zero vector 0, then the set of vectors can span R^ as long as the other vectors
are distinct.
n
B. If a set of vectors includes the zero vector 0, then the set of vectors spans R precisely when the set with 0
excluded spans Rª.
○ C. If a set of vectors includes the zero vector 0, then the set of vectors can span Rn as long as it contains n
vectors.
○ D. If a set of vectors includes the zero vector 0, then there is no reasonable way to determine if the set of vectors
spans Rn.
E. If a set of vectors includes the zero vector 0, then the set of vectors cannot span Rn.
F. none of the above
Assume {u1, U2, u3, u4} does not span R³.
Select the best statement.
A. {u1, U2, u3} spans R³ if u̸4 is a linear combination of other vectors in the set.
B. We do not have sufficient information to determine whether {u₁, u2, u3} spans R³.
C. {U1, U2, u3} spans R³ if u̸4 is a scalar multiple of another vector in the set.
D. {u1, U2, u3} cannot span R³.
E. {U1, U2, u3} spans R³ if u̸4 is the zero vector.
F. none of the above
Chapter 9 Solutions
Discrete Mathematics With Applications
Ch. 9.1 - A sample space of a random process or experiment...Ch. 9.1 - An event in a sample space is .Ch. 9.1 - To compute the probability of an event using the...Ch. 9.1 - Prob. 4TYCh. 9.1 - Toss two coins 30 times and make a table showing...Ch. 9.1 - In the example of tossing two quarters, what is...Ch. 9.1 - In 3-6 use the sample space given in Example...Ch. 9.1 - In 3-6 use the sample space given in Example...Ch. 9.1 - In 3-6 use the sample space given in Example...Ch. 9.1 - In 3-6 use the sample space given in Example...
Ch. 9.1 - In 7-10, use the sample space given in Example...Ch. 9.1 - In 7-10, use the sample space given in Example...Ch. 9.1 - In 7-10, use the sample space given in Example...Ch. 9.1 - In 7-10, use the sample space given in Example...Ch. 9.1 - Suppose that a coin is tossed three times and the...Ch. 9.1 - Suppose that each child born is equally likely to...Ch. 9.1 - Suppose that on a true/false exam you have no idea...Ch. 9.1 - There people have been exposed to a certain...Ch. 9.1 - Prob. 15ESCh. 9.1 - Two faces of a six-sided die are painted red, two...Ch. 9.1 - Prob. 17ESCh. 9.1 - Prob. 18ESCh. 9.1 - An urn contains two blue balls (denoted B1 and B2)...Ch. 9.1 - Relet to Example 9.1.3. Suppose you are appealing...Ch. 9.1 - Prob. 21ESCh. 9.1 - a. How many positive three-digit integers are...Ch. 9.1 - Suppose A[1],A[2],A[3],....,A[n] is a...Ch. 9.1 - Suppose A[1],A[2],...,A[n] is a one-dimensional...Ch. 9.1 - Suppose A[1], A[2],…A[n] is a one-dimensional...Ch. 9.1 - Prob. 26ESCh. 9.1 - What is the 62nd element in the one-dimensional...Ch. 9.1 - If the largest of 56 consecutive integers is 279,...Ch. 9.1 - Prob. 29ESCh. 9.1 - How many even integers are between 1 and 1,.001?Ch. 9.1 - Prob. 31ESCh. 9.1 - A certain non-leap year has 365 days, and January...Ch. 9.1 - Prove Theorem 9.1.1. (Let m be any integer and...Ch. 9.2 - The multiplication rule says that if an operation...Ch. 9.2 - A permutation of a set of elements is_________.Ch. 9.2 - Prob. 3TYCh. 9.2 - Prob. 4TYCh. 9.2 - Prob. 5TYCh. 9.2 - Prob. 6TYCh. 9.2 - Prob. 1ESCh. 9.2 - Prob. 2ESCh. 9.2 - Prob. 3ESCh. 9.2 - Prob. 4ESCh. 9.2 - Prob. 5ESCh. 9.2 - One urn contains two black balls (Labeled B1 and...Ch. 9.2 - One urn contains one blue ball (labeled B1) and...Ch. 9.2 - A person buying a personal computer system is...Ch. 9.2 - Suppose there are three roads from city A to city...Ch. 9.2 - Suppose there are three routes from North Point to...Ch. 9.2 - (a)A bit string is a finite sequence of 0’s and...Ch. 9.2 - Hexadecimal numbers are made using the sixteen...Ch. 9.2 - A coin is tossed four times. Each time the result...Ch. 9.2 - Suppose that in a certain stale, all automobile...Ch. 9.2 - A combination lock requires three selections of...Ch. 9.2 - a. How many integers are there from 10 through 99?...Ch. 9.2 - a. How many integers arc there from 1000 through...Ch. 9.2 - The following diagram shows the keypad for an...Ch. 9.2 - Three officers-a president, a treasurer, and a...Ch. 9.2 - Prob. 20ESCh. 9.2 - Suppose A is a set with m elements and B is a set...Ch. 9.2 - Prob. 22ESCh. 9.2 - In Section 2.5 we showed how integers can be...Ch. 9.2 - In each of 24—28, determine how many times the...Ch. 9.2 - In each of 24-28, determine how many times...Ch. 9.2 - Prob. 26ESCh. 9.2 - Prob. 27ESCh. 9.2 - Prob. 28ESCh. 9.2 - Consider the numbers 1 through 99,999 in their...Ch. 9.2 - Prob. 30ESCh. 9.2 - a. If p is a prime number and a is a positive...Ch. 9.2 - (a) How many ways can the letters of the word...Ch. 9.2 - Six people attend the theater together and sit in...Ch. 9.2 - Prob. 34ESCh. 9.2 - Write all the 2-permutations of {W,X,Y,Z}.Ch. 9.2 - Write all the 3-permutations of {s,t,u,v}.Ch. 9.2 - Evaluate the following quantities. a. P(6,4)b....Ch. 9.2 - a. How many 3-permutations are there of a set of...Ch. 9.2 - a. How many ways can three of the letters of the...Ch. 9.2 - Prove that for every integer n2. P(n+1,3)=n3nCh. 9.2 - Prob. 41ESCh. 9.2 - Prob. 42ESCh. 9.2 - Prob. 43ESCh. 9.2 - Prove Theorem 9.2.1 by mathematical induction.Ch. 9.2 - Prove Theorem 9.2.2 by mathematical induction.Ch. 9.2 - Prob. 46ESCh. 9.2 - Prob. 47ESCh. 9.3 - The addition rule says that if a finite set A...Ch. 9.3 - Prob. 2TYCh. 9.3 - Prob. 3TYCh. 9.3 - Prob. 4TYCh. 9.3 - Prob. 5TYCh. 9.3 - (a) How many bit string consist of from one...Ch. 9.3 - (a) How many string of hexadecimal digits consist...Ch. 9.3 - (a) How many integers from 1 through 999 do not...Ch. 9.3 - How many arrangements in a row of no more than...Ch. 9.3 - (a) How many five-digit integers (integers from...Ch. 9.3 - In a certain stale, all license plain consist of...Ch. 9.3 - At a certain company, passwords must be from...Ch. 9.3 - In a certain country license plates consist of...Ch. 9.3 - a. Consider the following algorithm segment: for...Ch. 9.3 - A calculator has an eight-digit display and a...Ch. 9.3 - a. How many ways can the letters of the word QUICK...Ch. 9.3 - (a) How many ways can the letters of the word...Ch. 9.3 - A group of eight people are attending the movies...Ch. 9.3 - Prob. 14ESCh. 9.3 - Prob. 15ESCh. 9.3 - Prob. 16ESCh. 9.3 - (a) How many string of four hexadecimal digits do...Ch. 9.3 - Prob. 18ESCh. 9.3 - A combination lock requires three selections of...Ch. 9.3 - (a) How many integers from 1 through 100,000...Ch. 9.3 - Prob. 21ESCh. 9.3 - Consider strings of length n over the set {a, b,...Ch. 9.3 - (a) How many integers from 1 through 1,000 are...Ch. 9.3 - (a) How many integers from 1 through 1,000 are...Ch. 9.3 - Prob. 25ESCh. 9.3 - Prob. 26ESCh. 9.3 - For each integer n0 . let akbe the number of bit...Ch. 9.3 - Prob. 28ESCh. 9.3 - Refer to Example 9.3.5. Write the following IP...Ch. 9.3 - A now in a classroom has n seats. Let sn be the...Ch. 9.3 - Assume that birthdays are equally likely to occur...Ch. 9.3 - Assuming that all years have 365 days and all...Ch. 9.3 - A college conducted a survey to explore the...Ch. 9.3 - A study was done to determine the efficacy of...Ch. 9.3 - Prob. 35ESCh. 9.3 - Prob. 36ESCh. 9.3 - Prob. 37ESCh. 9.3 - Prob. 38ESCh. 9.3 - Prob. 39ESCh. 9.3 - Prob. 40ESCh. 9.3 - For 40 and 41, use the definition of the Euler phi...Ch. 9.3 - Prob. 42ESCh. 9.3 - Prob. 43ESCh. 9.3 - Prob. 44ESCh. 9.3 - Prob. 45ESCh. 9.3 - Prob. 46ESCh. 9.3 - Prob. 47ESCh. 9.3 - Prob. 48ESCh. 9.3 - Prob. 49ESCh. 9.4 - The pigeonhole principle states that_______Ch. 9.4 - The generalized pigeonhole principle states that...Ch. 9.4 - If X and Y are finite sets and f is a function...Ch. 9.4 - A small town has only 500 residents. Must there be...Ch. 9.4 - In a group of 700 people, must there be 2 who have...Ch. 9.4 - (a) Given any set of four integers, must there be...Ch. 9.4 - (a) Given any set of seven integers, must there be...Ch. 9.4 - Let S={3,4,5,6,7,8,9,10,11,12} . Suppose six...Ch. 9.4 - Let T={1,2,3,4,5,6,7,8,9}. Suppose five integers...Ch. 9.4 - (a) If seven integers are chosen from between 1...Ch. 9.4 - If n+1 integers are from the set {1,2,3,...2n}....Ch. 9.4 - If n+1 integers are chosen from the set...Ch. 9.4 - Prob. 12ESCh. 9.4 - Suppose six pairs of similar-looking boots are...Ch. 9.4 - Prob. 14ESCh. 9.4 - If n is a positive integer, how many integers from...Ch. 9.4 - How many integer from 1 through 100 must you pick...Ch. 9.4 - Prob. 17ESCh. 9.4 - How many integers must you pick in order to be...Ch. 9.4 - How many integers from 100 through 999 must you...Ch. 9.4 - Prob. 20ESCh. 9.4 - When 683/1493 is written as a decimal what is the...Ch. 9.4 - Prob. 22ESCh. 9.4 - Prob. 23ESCh. 9.4 - Show that within any set of thirteen integers...Ch. 9.4 - Prob. 25ESCh. 9.4 - Prob. 26ESCh. 9.4 - In a group of 2,000 people, must at least 5 have...Ch. 9.4 - A programmer writes 500 lines of computer code in...Ch. 9.4 - A certain collage class has 40 students. All the...Ch. 9.4 - A penny collection contains twelve 1967 pennies,...Ch. 9.4 - A group of 15 exeutives are to share 5 assistants....Ch. 9.4 - Prob. 32ESCh. 9.4 - Prob. 33ESCh. 9.4 - Let S be a set of ten integers chosen from 1...Ch. 9.4 - Prob. 35ESCh. 9.4 - Show that if 101 integers are chosen from 1 to 200...Ch. 9.4 - a. Suppose a1,a2,...,an is a sequence of n...Ch. 9.4 - Prob. 38ESCh. 9.4 - What is the largest number of elements that a set...Ch. 9.4 - Prob. 40ESCh. 9.5 - Prob. 1TYCh. 9.5 - The number of r-combinations of a set of n...Ch. 9.5 - Prob. 3TYCh. 9.5 - Prob. 4TYCh. 9.5 - Prob. 5TYCh. 9.5 - Prob. 1ESCh. 9.5 - Prob. 2ESCh. 9.5 - Prob. 3ESCh. 9.5 - Write an equation relating P(8,3) and (38) .Ch. 9.5 - Use Theorem 9.5.1 to compute each of the...Ch. 9.5 - A student council consists of 15 students. a. In...Ch. 9.5 - A computer programming team has 13 members. a. How...Ch. 9.5 - An instructor gives an exam with fourteen...Ch. 9.5 - A club is cosidering changing its bylaws. In an...Ch. 9.5 - Two new drugs -ire to be tested using a group of...Ch. 9.5 - Refer to Example 9.5.9. For each poker holding...Ch. 9.5 - How many pairs of two distinct integers chosen...Ch. 9.5 - A coin is tossed ten times. In each case the...Ch. 9.5 - (a) How many 16-bit strings contain exactly seven...Ch. 9.5 - (a) How many even integer are in the set...Ch. 9.5 - Suppose that three microchips in a production run...Ch. 9.5 - Ten points Libeled A. B. C. D. E. F. G. H, I. J...Ch. 9.5 - Prob. 18ESCh. 9.5 - (a) How many distinguishable ways can the letters...Ch. 9.5 - a. How man distinguishable ways can the letters...Ch. 9.5 - In Morse code, symbols are represented by...Ch. 9.5 - Each symbol in the Braile code is represented by a...Ch. 9.5 - On an 88 chessboard, a rook is allowed to move any...Ch. 9.5 - The number 42 has the prime factorization 237 ....Ch. 9.5 - a. How many one-of-one functions ant there from a...Ch. 9.5 - a. How many onto functions are there from a set...Ch. 9.5 - Let A be a set with eight elements. How many...Ch. 9.5 - A student council consists of three freshmen, four...Ch. 9.5 - Prob. 29ESCh. 9.5 - Prob. 30ESCh. 9.6 - Given a set X={x1,x1,,xn} , an r-combination with...Ch. 9.6 - Prob. 2TYCh. 9.6 - Prob. 3TYCh. 9.6 - (a) According to Theorem 9.6.1, how many...Ch. 9.6 - (a) According to Theorem 9.6.1, how many multisets...Ch. 9.6 - A bakery produces six different kinds of pastry,...Ch. 9.6 - A camera shop stocks eight different types of...Ch. 9.6 - If n is a positive integer, how many 4-tuples of...Ch. 9.6 - If n is a positive integer, how many 5-tuples of...Ch. 9.6 - Prob. 7ESCh. 9.6 - Prob. 8ESCh. 9.6 - In 8 and 9, how many times will the innermost loop...Ch. 9.6 - Prob. 10ESCh. 9.6 - Prob. 11ESCh. 9.6 - Prob. 12ESCh. 9.6 - In 10-14, find how many solutions there are to the...Ch. 9.6 - In 10-14, find how many solutions there are to the...Ch. 9.6 - Prob. 15ESCh. 9.6 - Consider the situation in Example 9.6.2. a....Ch. 9.6 - a. A store sells 8 colors of balloons with at...Ch. 9.6 - A large pile of coins consists of penruey nickels,...Ch. 9.6 - Suppose the bakery in exercise 3 has at least...Ch. 9.6 - Suppose the camera shop in exercise 4 can obtain...Ch. 9.6 - Prob. 21ESCh. 9.7 - If n and r are nonnegative integers with rn , then...Ch. 9.7 - Prob. 2TYCh. 9.7 - Prob. 3TYCh. 9.7 - Prob. 4TYCh. 9.7 - Prob. 5TYCh. 9.7 - Prob. 6TYCh. 9.7 - Prob. 7TYCh. 9.7 - Prob. 1ESCh. 9.7 - Prob. 2ESCh. 9.7 - Prob. 3ESCh. 9.7 - Prob. 4ESCh. 9.7 - Prob. 5ESCh. 9.7 - Prob. 6ESCh. 9.7 - Prob. 7ESCh. 9.7 - Prob. 8ESCh. 9.7 - Prob. 9ESCh. 9.7 - (a) Use Pascal’s triangle given in Table 9.7.1 to...Ch. 9.7 - Prob. 11ESCh. 9.7 - Use Pascal’s formula repeatedly to derive a...Ch. 9.7 - Use Pascal’s formula to prove by mathematical...Ch. 9.7 - Prob. 14ESCh. 9.7 - Prove the following generalization of exercise 13:...Ch. 9.7 - Prob. 16ESCh. 9.7 - Prove that for every integer n0 ,...Ch. 9.7 - Prob. 18ESCh. 9.7 - Prob. 19ESCh. 9.7 - Prob. 20ESCh. 9.7 - Prob. 21ESCh. 9.7 - Use the binomial theorem to expand the expressions...Ch. 9.7 - Use the binomial theorem to expand the expressions...Ch. 9.7 - Use the binomial theorem to expand the expressions...Ch. 9.7 - Prob. 25ESCh. 9.7 - Prob. 26ESCh. 9.7 - Prob. 27ESCh. 9.7 - Prob. 28ESCh. 9.7 - Prob. 29ESCh. 9.7 - Prob. 30ESCh. 9.7 - In 29-34, find the coefficient of the given term...Ch. 9.7 - In 29-34, find the coefficient of the given term...Ch. 9.7 - Prob. 33ESCh. 9.7 - In 29-34, find the coefficient of the given term...Ch. 9.7 - Prob. 35ESCh. 9.7 - For every integer n1 ,...Ch. 9.7 - Prob. 37ESCh. 9.7 - Prob. 38ESCh. 9.7 - Prob. 39ESCh. 9.7 - Prob. 40ESCh. 9.7 - Prob. 41ESCh. 9.7 - Prob. 42ESCh. 9.7 - Prob. 43ESCh. 9.7 - Prob. 44ESCh. 9.7 - Prob. 45ESCh. 9.7 - Prob. 46ESCh. 9.7 - Prob. 47ESCh. 9.7 - Prob. 48ESCh. 9.7 - Prob. 49ESCh. 9.7 - Prob. 50ESCh. 9.7 - Express each of the sums in 43—54 in closed form...Ch. 9.7 - Prob. 52ESCh. 9.7 - Prob. 53ESCh. 9.7 - Prob. 54ESCh. 9.7 - Prob. 55ESCh. 9.8 - If A is an event in a sample space S,P(A) can...Ch. 9.8 - Prob. 2TYCh. 9.8 - Prob. 3TYCh. 9.8 - Prob. 4TYCh. 9.8 - Prob. 5TYCh. 9.8 - Prob. 1ESCh. 9.8 - Prob. 2ESCh. 9.8 - Prob. 3ESCh. 9.8 - Prob. 4ESCh. 9.8 - Prob. 5ESCh. 9.8 - Prob. 6ESCh. 9.8 - Prob. 7ESCh. 9.8 - Prob. 8ESCh. 9.8 - Let A and B be events in a sample space S, and let...Ch. 9.8 - Prob. 10ESCh. 9.8 - Prob. 11ESCh. 9.8 - Prob. 12ESCh. 9.8 - Prob. 13ESCh. 9.8 - A lottery game offers $2 million to the grand...Ch. 9.8 - A company offers a raffle whose grand prize is a...Ch. 9.8 - An urn contains four balls numbered 2, 2, 5, and...Ch. 9.8 - Prob. 17ESCh. 9.8 - An urn contains five balls numbered 1,2,2,8, and...Ch. 9.8 - Prob. 19ESCh. 9.8 - Suppose a person offers to play a game with you....Ch. 9.8 - Prob. 21ESCh. 9.8 - Prob. 22ESCh. 9.8 - Prob. 23ESCh. 9.9 - Prob. 1TYCh. 9.9 - Prob. 2TYCh. 9.9 - Prob. 3TYCh. 9.9 - Prob. 4TYCh. 9.9 - Prob. 1ESCh. 9.9 - Prob. 2ESCh. 9.9 - Prob. 3ESCh. 9.9 - Prob. 4ESCh. 9.9 - Suppose that A and B are events in a sample space...Ch. 9.9 - An urn contains 25 red balls and 15 blue balls....Ch. 9.9 - Prob. 7ESCh. 9.9 - A pool of 10 semifinalists for a job consists of 7...Ch. 9.9 - Prob. 9ESCh. 9.9 - Prob. 10ESCh. 9.9 - One urn contains 12 blue balls and 7 white balls,...Ch. 9.9 - Redo exercise 11 assuming that the first urn...Ch. 9.9 - Prob. 13ESCh. 9.9 - Prob. 14ESCh. 9.9 - Prob. 15ESCh. 9.9 - Three different supplier.-X, Y. and Z-provide...Ch. 9.9 - Prob. 17ESCh. 9.9 - Prob. 18ESCh. 9.9 - Prob. 19ESCh. 9.9 - Prob. 20ESCh. 9.9 - Prob. 21ESCh. 9.9 - Prob. 22ESCh. 9.9 - Prob. 23ESCh. 9.9 - Prob. 24ESCh. 9.9 - A coin is loaded so that the probability of heads...Ch. 9.9 - Describe a sample space and events A,B, and C,...Ch. 9.9 - Prob. 27ESCh. 9.9 - Prob. 28ESCh. 9.9 - Suppose that ten items are chosen at random from a...Ch. 9.9 - Suppose the probability of a false positive result...Ch. 9.9 - Prob. 31ESCh. 9.9 - Prob. 32ESCh. 9.9 - Prob. 33ESCh. 9.9 - Prob. 34ES
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- Which of the following sets of vectors are linearly independent? (Check the boxes for linearly independent sets.) ☐ A. { 7 4 3 13 -9 8 -17 7 ☐ B. 0 -8 3 ☐ C. 0 ☐ D. -5 ☐ E. 3 ☐ F. 4 THarrow_forward3 and = 5 3 ---8--8--8 Let = 3 U2 = 1 Select all of the vectors that are in the span of {u₁, u2, u3}. (Check every statement that is correct.) 3 ☐ A. The vector 3 is in the span. -1 3 ☐ B. The vector -5 75°1 is in the span. ГОЛ ☐ C. The vector 0 is in the span. 3 -4 is in the span. OD. The vector 0 3 ☐ E. All vectors in R³ are in the span. 3 F. The vector 9 -4 5 3 is in the span. 0 ☐ G. We cannot tell which vectors are i the span.arrow_forwardTrolley of the overhead crane moves along the bridge rail. The trolley position is measured from the center of the bridge rail (x = 0) is given by x(t) = 0.5t^3-6t^2+19.5t-14 : 0 <= t <= 3 min. The trolley moves from point A to B in the forward direction, B to C in the reverse direction and C to D again in the forward direction. CONTROL PANEL END TRUCK- RUNWAY BEAM- BRIDGE RAIL HOIST -TROLLEY TROLLEY BUMPER TROLLEY DRIVE LPENDANT TRACK -TROLLEY CONDUCTOR TRACK WIRE ROPE -HOOK BLOCK -BRIDGE DRIVE -END TRUCK BUMPER -RUNWAY RAIL TROLLEY END STOP -CONDUCTOR BAR PENDANT FESTOONING TROLLEY FESTOONING PENDANT CABLE PENDANT x(t)=0.5t^3-6t^2+19.5t-14 v(t)=1.5t^2-12t+19.5 a(t)=(dv(t))/dt=3t-12 Fig. T2.2: The overhead crane Total masses of the trolley, hook block, and the load attached to the hook block are 110 kg, 20 kg, and 150 kg. Damping coefficient, D, is 40 kg/s. What is the total amount of energy required from the trolley motor to move the system [Hint: Use Newton's 2nd law to obtain the…arrow_forward
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Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Probability & Statistics (28 of 62) Basic Definitions and Symbols Summarized; Author: Michel van Biezen;https://www.youtube.com/watch?v=21V9WBJLAL8;License: Standard YouTube License, CC-BY
Introduction to Probability, Basic Overview - Sample Space, & Tree Diagrams; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=SkidyDQuupA;License: Standard YouTube License, CC-BY