22] calculate the number of combination and permutation of, 5 distinct objects taken 2 at time?

Q: 3. Find the number of distinct permutations that can be formed your ID number.

A:

Q: How many ways are there to distribute eight balls into six distinct boxes with at least one ball in…

A: The balls are identical. In this case there are 8 balls and 6 boxes to be placed, so each box can be…

Q: 2) Each type of machine part made in a factory is stamped with a code of the form…

A: We can use :- 26 letters, 10 digits, 10 digits (as digits can be repeated)   Total number of…

Q: 2. Civil Engineers at a large convention are offered 6 construction tours on each of 3 days. In how…

A: Given : Number of tours = 6 Number of days = 3

Q: 7. In how many ways can seven men and six women be arranged in a row so that the women occupy the…

A: Given, In an arrangement,Total men=7Total women=6 To find: Total ways of arrangement so that women…

Q: 8. The number of permutations of 11 objects taken 4 at a time is ---

A: Solution :  we have to find number of permutations of 11 objects taken 4 at a time.

Q: A staff number of a BigHit company is composed of 2 non-vowels uppercase alphabets and 3 digit…

A: GivenA staff number of a BigHit company is composed of 2 non-vowelsuppercase alphabets and 3 digit…

Q: 5. How many 2-permutations are there of a set of eight objects?

A: We know that,  The formula pf permutations is,  nPr = P(n, r) = n!/(n-r)!

Q: How many ways are there to assign 100 different diplomats to five different conti- nents if 10…

A: Here,  total diplomats = 100 Number of continents= 5 Also, in continent 1, 2 ,3,4,5 there sholud be…

Q: How many permutations π of [10] satisfy π^5 = 1?

A: The given set is 10=1,2,3,…,10. Therefore any permutation π of 10, is bijective function from the…

Q: Suppose that 11 children collected 50 books. Prove by contradiction that at least two of them had…

A: In mathematics, proof by contradiction is a method of proving something by assuming opposite of what…

Q: 5. How many strings of 3 characters are there, such that every character is a lower case letter, the…

A: If there are a ways of doing something and b ways of doing another thing, then there are a · b ways…

Q: 5. Bayes' theorem provides a way to

A: #Bayes' theorem used in case of conditional probability i.e when prior probability of events are…

Q: 2) Allowing (or requiring) users to use numerical digits (including 0) and one of 31 "special…

A: Introduction: Considering the lower- and upper-case alphabets to be two different characters, total…

Q: 1) How many different strings of 5 lower case letters are there? Assume that letters may repeat. 2)…

A: Here, to calculate number of different strings of 5 lower case letters can be created if that…

Q: A box contain 8 red and 6 green balls. In how many ways can 3 balls be drawn such that they are all…

A:

Q: 6. How many different 3-digit identification tags can be made if the digits can be used more than…

A: Note- Since both are different questions, so according to our policy we can answer only one…

Q: (3) Find the formula for the number of ways for putting n identical balls into k distinct boxes so…

A:

Q: Find the number of permutations using four different numbers (2,5,11,30) if they are taken 2 at a…

A: Given that, Four different numbers are (2,5,11,30) To find: Number of permutations using four…

Q: Determine the number of ways in which the four corners of a squarecan be colored with two colors.…

A:

Q: show that number of 132- avoiding permutations are equal to number of 123-avoiding permutations

A: We have to show that number of 132- avoiding permutations are equal to number of 123-avoiding…

Q: 1. How many distinguishable ways can the letters of the word MILLIMICRON be arranged in order?

A: According to our guidelines, We can answer only first question.

Q: In how many ways 4 fruits (of any type) can be picked up from a basket of fruits containing 3 types:…

A: Given Information Basket contains 3 types of Fruits: Apples, Oranges and Pears 4 fruits is to be…

Q: 7. Find out the number of ways in which 6 rings of different types can be worn in 3 fingers?

A:

Q: 3. How many ways are there to distribute n identical balls in k distinguishable (labelled) boxes…

A: It is given that there are n identical balls in k distinguishable boxes.

Q: In how many ways can 16 balls be drawn from an urn containing 3 red balls, 8 white balls, and 5 blue…

A: We have given that,  Red balls = 3  White balls= 8  Blue  balls= 5 Then,  We wil find the how many…

Q: Use pigeonhole principle 1. How many numbers must be selected from the set {1, 3, 5, 7, 9, 11, 13,…

A:

Q: In how many ways can we distribute eight identical white balls into four distinct containers so that…

A:

Q: Find the number of distinguishable permutations of: 6 Ds, 5 Js, and 2 Os

A: our objective is to find the no. of permutations

Q: 11. What is the sum of all 4 digit numbers formed using the digits 2, 3,4 and 5 without repetition?

A:

Q: An Uber XL can hold between 1 and 4 people. One September evening, 5 distinct and random people need…

A: According to the given information, An uber XL can hold between 1 and 4 people. On September evening…

Q: How many words can be formed by permutation of the letters of the word DEPRESSION such that each…

A: Given word DEPRESSION We have to calculate No. Of words such that obtained word does not contain 2…

Q: Suppose there are balls of 6 different colors, i.e., Red, Blue, Green, Yellow, Black, and Brown, in…

A: given total number of color of balls =6 also, there are exactly 25 indistinguishable balls of each…

Q: Suppose there are 10 students participating in a workshop that meets every day of a five-day work…

A: Given that there are 10 students participating in a workshop that meets every day of a five-day work…

Q: (a) How many 4-permutations are there of a set of six objects? (b) How many 2-permutations are there…

A:

Q: er

A: To find all the permutations of the 4 objects a ,b, c, and d, taken 3 at a time.

Q: How many three-digit numbers with different digits are there, formed from digits belonging to the…

A: The given digits are : 1,2,3,4,5,6,7,8,9 The total no. of digits given = 9 We are required to form a…

Q: Number of circular permutations of different .!things taken all at a time is (n-1)

A:

Q: A box contain 8 red and 6 green balls. In how many ways can 3 balls be drawn such that 2 is ed and 1…

A: Answer - A box contains 8 red and 6 green balls.                 How many ways can 3 balls be drawn…

Q: There are 5 pocket holes at the periphery of a round horizontal platform. In how many ways can 5…

A:

Q: . Find the number of permutations of the letters of the word ‘REMAINS’ such that the vowels always…

A: We can solve these questions using given details

Q: Find the number of distinguishable permutations of: 4 Ds, 6 Hs, and 2 Os

A: Simply use the permutations of n letters in which r letters are identical.

Q: How Many perMutations of the digits 0, I, 2, 3. 4, 5, 6, 7, 8, 9 are there in which the digitss…

A: The permutation represents the number of ways something can be arranged. In permutations or…

Q: How many permutations of {1, 2, 3, 4, 5, 6, 7} leave exactly 1 element fixed?

A:

Q: 3. In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels…

A: The word OPTICAL has three vowels O,I and A. Consider these three letters as 1 and the remaining…

Q: Find the number of distinguishable permutations of the digits of the number 3,283,882,432,599

A: The number of distinguishable permutations is 3,283,882,432,599.

Q: 2) Find the number of distinguishable permutations of the digits of the number 911 912 271. 3) In…

A:

Q: 2.21 Registrants at a large convention are offered 6 sightseeing tours on each of 3 days. In how…

A: Given: Number of sight seeing offered=6 Number of days of tour=3 Determine the number of ways in…

Q: 1. Taking into account identical letters, how many ways are there to arrange the word HUDSONICUS…

A: As per honor code, we are entitled to solve only 1 question at a time so I am providing the same.…

Q: How many permutations of {1, 2, 3, 4, 5, 6, 7, 8) leave exactly 1 element fixed?

A:

Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.