A shop has 6 types of candy. How many ways are there to select 24 pieces of candy with at least two of each kind being selected and repetition allowed?

Q: A jar contains 5 white balls, 8 black balls, and 6 red balls. In how many ways can 5 balls be…

A:

Q: Two coins are randomly drawn from a coin pouch. If there are 5 dimes, 2 nickels, and a quarter, how…

A: As given there are 5 dimes, 2 nickels, and a quarter in a pouch. 1 nickel = 5 cents 1 dime = 10…

Q: Consider the five letters a,b,c,d,e. In how many distinct ways can three letters be selected and…

A: Permutation:         The act of arranging the members of a set into an order or sequence, if it is…

Q: A restaurant offers a special pizza with any 5 toppings. If the restaurant has 13 toppings from…

A: Combination: The number of different selections of ‘r’ elements (order doesn’t matter) from a set of…

Q: Two coins are randomly drawn from a coin pouch. If there are 4 dimes, 2 nickels, and a quarter, how…

A: The pouch contains 4 dimes, 2 nickels and one quarter. Two coins are randomly drawn from a pouch.

Q: How many combinations can the seven colors of the rainbow be arranged into groups of three colors…

A:

Q: Two coins are randomly drawn from a coin pouch. If there are 4 dimes, 3 nickels, and a quarter, how…

A: The probability density function of X is obtained below:From the given information, number of coins…

Q: How many 5 letter "words" can be formed if exactly 2 of the letters are vowels if repetition is…

A:

Q: how many ways can five persons line up to get on a bus?

A: The number of persons is 5.

Q: A box contains 8 red balls, 8 blue balls, and 6 orange balls. In how many ways can 6 balls be chosen…

A: Given : A box contains 8 red balls, 8 blue balls, and 6 orange balls

Q: Suppose that a candy shop sells eight different kinds of candies: 50 cherry, 50 strawberry, 40…

A: Total number of candies = 310 Number of candies to be selected = 7

Q: How many five-card poker hands containing exactly one pair are possible from a deck of 52 cards?

A: To find n(S), determine the number of ways to choose five-card hands from a pack of 52 cards.…

Q: A State's License plates consist of 4 letters followed by 5 digits. How many possible license plates…

A: Given,  License plate consist of 4 letters followed by 5 digits. Since repetition of the letters and…

Q: A race has 10 runners. In how many ways can the first three places be decided?

A: Here use combination

Q: . A shipment of 50 calculators contains 3 that are defective. In how many ways can an inspector…

A: we have to find number  of ways..

Q: A family has 4 children.  How many different boy/girl orders are possible?

A: When a family has a child there are two possibilities either a boy or a girl.

Q: A student is given a reading list of eight books from which he must select two for an outside…

A: A student is given a reading list of eight books from which he must select two for an outside…

Q: The number of permutation of n items is also called as _______________.

A: We have to fill the blank with the correct information -  The number of permutation of n items is…

Q: Assuming that no one can hold more than one office, how many selections are possible?

A: select a president, vice-president, secretary, and treasurer out of a club with 15 members.  Here…

Q: b) Suppose that repetition of letters is pemitted, How many 6 letter can be fomed from the letters?

A: Now we have to calculate ,how many 6 letter can be formed if repetition is permitted.

Q: You are ordering an extra large pizza with multiple toppings on it. In how many ways can 6 different…

A:

Q: How many ways are there to pair 2n people?

A: We need to compute the number of ways in which 2n people can be paired.

Q: A shipment of 40 computers are unloaded from the van and tested 6 of them are defective In how many…

A: We will find out the required number of ways.

Q: In a shipment of  59 vials, only 14 do not have hairline cracks. If you randomly select 2 vials from…

A: Given that  Number of vials (n) = 59 Vials do not have hairline cracks = 14 Vials having hairline…

Q: Each telephone number in a city consists of 7 digits, the first of which must be 3 or 4. (a) How…

A: HERE TELEPHONE Diary consists of 7 digits, first is either 3 or 4.

Q: In how many different ways can the director of a research laboratory choose two chemists from among…

A: Solution: Given information: Chemists applicants = 11  Physicists applicants = 7   To choose 2…

Q: Certain automobile license plates consist of a sequence of three letters followed by four digits. If…

A: We have a license plate that consists of a sequence of three letters followed by four digits. The…

Q: Six players are to be selected from an 11​-player baseball team to visit schools to support a summer…

A: No. Of total students = 11 No. Of player to select = 6.

Q: In a certain beauty pageant, there are 10 equally beautiful and talented candidates. In how many…

A:

Q: How many possible ways can the top 5 finishers come in during a race with 24 racers? Each place…

A: This is a permutation problem.   Out of the 24, there will be 5 racers in the top 5.

Q: In how many ways can a group of 5 girls be selected from 8 if the eldest girl is included in each…

A: The formula for combination is nCr = n! / [r! (n – r)!] = [n (n – 1) … (n – r + 1)]/r!. Explanation:…

Q: There are 14 students in the club. How many ways can a group of more than 11 students be chosen?

A:

Q: 1. In your drawer, there are 6 identical pairs of purple socks, 7 identical pairs of polka dot…

A:

Q: You are ordering an extra large pizza with multiple toppings on it. In how many ways can 8 different…

A:

Q: A state makes a license plate with 3 letters followed by 5 numbers. If repetitions are permitted,…

A: To find the different ways in which license plates can be made

Q: In how many ways can a person choose three movies to watch from a collection of 7 suggested movies?

A: The formula for combination is nCr= n! / [r! (n – r)!] = [n (n – 1) … (n – r + 1)] / r!.…

Q: The number of permutations of n items is also called as _______________.

A: The number of permutations of n items is also called as n! (n Factorial).

Q: A cargo ship unloaded a shipment of 12 photocopy machines that contains 3 defective units. In how…

A:

Q: A track race has 6 participants. In how many orders could the runners possibly finish

A:

Q: How many different selections of three books can be made from a set of fifteen books?

A: Introduction:According to the permutation rule, if r distinct items are to be chosen from n items…

Q: In how many ways can six pictures be selected from a group of ten different pictures?

A: It is given that 6 different pictures are to be selected from a group of 10 pictures, therefore,

Q: In a group of 6 boys and 4 girls, 4 children are to be selected. In how many ways can they be…

A: The number of ways in which r different items can be selected from n different items, can be given…

Q: There are 10 defective light bulbs in a bin containing 25 light bulbs. In how many ways can you…

A:

Q: Suppose a certain combination lock requires three selections of numbers, each from 1 through 25.…

A: 1 to 25 there are 25 numbers. The numbers may repeat in the combination. For the first number, there…

Q: In how many ways can five pictures be selected from a group of nine different pictures?

A:

Q: Suppose you are asked to choose three movies. If there are 20 different movies, in how many ways can…

A: According to the combination rule, if r distinct items are to be chosen from n items without…

Q: How many ways are there to select 5 cookies from a jar containing 3 types when repetition is…

A: Theorem-  there are C(n+r-1 , r) ways of choosing r-combination from a set of n elements when…

Q: A teacher will randomly award three students with extra credit. How many possible ways can the…

A: Given that  , a teacher will randomly award three students with extra credit .  Teacher can pick…

Q: A shipment of 40 computers are unloaded from the van and tested. 6 of them are defective. In how…

A:

Q: In how many ways can 3 students be selected from a group of 12 students to represent a university in…

A: Given data: Total students = 12 3 students  selected  randomly To find: In how many ways can 3…

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.