A box of colored crayons contains 15 distinct colors. In how many ways can 4 colors be chosen,  assuming that the order of the colors chosen doesn't matter?

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

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Q: The eleven players of the CHS sepak takraw team are to be photographed for the team's tarpaulin. In…

A: Here, the question is in how many ways can 11 players can be arranged in a row.

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

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

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Q: If a person can select five books from a list of ten, how many different combinations are there?

A: Given data: The total numbers of books are n=10. The number of books selected is r=5. The expression…

Q: There are 10 students in a class. In how many ways can an instructor give at most three students a…

A: n = 10 Let x represent the number of students given grade A.   The number of ways a student can be…

Q: From a club of 17 people, in how many ways can a group of six members be selected to attend a…

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Q: A store sells 8 kinds of balloons with at least 30 of each kind. How many different combinations of…

A: 8 kinds of balloons with at least 30 of each kind We have to find how many different combinations of…

Q: In how many ways can 9 individuals be seated in a row of 9 chairs if two individuals wanted to be…

A: Permutation is the method that used to measure the number of arrangement in the data set. In this…

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: How many different arrangements can be made using all the letters in VANCOUVER?

A: There are total 9 letters in the word VANCOUVER. Letter Frequency V 2 A 1 N 1 C 1 O 1…

Q: A sales assistant is hanging 11 sweaters on a rack. He has 3 brown sweaters, 2 gray sweaters, and 6…

A: From the provided information Total sweaters = 11 Brown sweaters = 3 Gray sweaters = 2 Green…

Q: In a friend group of six, how many ways can we arrange them in a line for a photograph?

A: In a friend group of six, we have to arrange them in a line for a photograph.

Q: A sales assistant is hanging 11 sweaters on a rack. He has 5 white sweaters, 4 brown sweaters, and 2…

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Q: In a deck of 52 playing cards, how many 4-card hands are there that are made up of only red cards?

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Q: In a bag of Jolly Gems candy-coated chocolate pieces, 26% are red, 21% are blue, 15% are brown, 16%…

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Q: How many different ways can 5 out of 8 different shirts, 4 out of 10 different pieces of slacks, and…

A: Different ways can  5 out of 8 different shirts, 4 out of 10 different pieces of slacks, and 3 out…

Q: There are 11 goldfish in a fishpond. In how many ways can 5 be chosen to be moved to another…

A: →Whenever, we have to select r things without knowing order of selection    from n things , then…

Q: Suppose you are asked to list, in order, the three best movies you have seen this year. If you saw…

A: Suppose you are asked to list, in order of preference, the three best movies you have seen this…

Q: Ten jokes are listed in a magazine.   If the fourth joke from the magazine is​ excluded, in how…

A: There are 10 jokes listed in a magazine.Here 4th joke is excluded than find the number of ways…

Q: There are 10 students in a class. In how many ways can an instructor give at least one student a…

A: There are 10 students So sample size, n= 10 And we've to find ways for at least 1 student. So r= 1

Q: How many different patchwork quilts, four patches long and three patches wide, can be made from five…

A: Given: Five red and seven blue squares.   To determine: The number of different patchwork quilts…

Q: From a list of 34 captains, 6 are to be promoted to major. In how many ways can this be done?

A: To write that in how many ways it can be done

Q: How many 5-number license plates can be made using the digits: 0, 1, 2, 3, 4, 5, if repetitions are…

A: Given that 5-number license plates that are made using digits 0, 1, 2, 3, 4, 5. We have to determine…

Q: There are 10 people in a meeting. In how many ways can you arrange your participants around a ROUND…

A: Total ways in which 10 people be arranged around a round table so that 4 people sit beside each…

Q: Suppose we want to choose 5 colors, without replacement, from 14 distinct colors. (a) If the order…

A: Suppose we want to choose 5 colors without replacement from 14 distinct colors

Q: How many different sets of 6 cards each can be formed from a standard deck of 52 cards?

A: Please find attachment for the details solution

Q: In how many ways can three taxi drivers be assigned to nine cars?

A: The number of taxi drivers is 3 and the number of cars is 9.

Q: If repetitions are not permitted, from the 6 digits 0, 2, 3, 4, 5, and 8, how many 4- digit number…

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Q: a restauranr offers 4 different flavors of coffee,3 different soup selections and 4 different…

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Q: A sailboat owner received 5 different signal flags with his new sailboat. If the order in which the…

A: Given A sailboat owner received 5 different signal flags with his new sailboat.

Q: There are five people at a volleyball tournament. In how many ways can a team of three be chosen?

A: The number of ways r items can be chosen out of n items is equal to C(n,r) . The formula for C(n,r)…

Q: Suppose we want to choose 2 colors, without replacement, from the 5 colors red, blue, green, purple,…

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Q: How many different sets of 5 cards can be formed from a standard deck of 52 cards?

A: We need to find the number of different 5 card sets that can be formed from a deck of 52 cards. Now,…

Q: Five cards are selected out of 52. In how many different ways can this be done if: they contain the…

A: total cards are 52 cards.  they are 13 clubs , 13 spades , 13 hearts ,13 diamonds clubs and spades…

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: If 5 horses are in a race and they all finish with no ties, in how many ways can the horses finish…

A: Given information- We have given that 5 horses are in a race. They all finish the race with no ties.…

Q: you have 11 tubs of paint how many distinct color groupings can you make with your paint?

A: Total given colors are   11 Total distinct colors grouping   ?   we can solve this question with the…

Q: From a group of 20 people, 12 are selected to serve on a jury during a trial. How many different…

A: The total number of combinations possible if we select r things which are chosen at a time  from n…

Q: Your sister is shopping at an exclusive Rodeo Drive clothing store and examines 4 distinct blouses,…

A: It is given that there are 4 distinct blouses, 5 distinct dresses, and 2 distinct handbags. Since,…

Q: In how many different ways can 4 passengers be seated in an airplane if each passenger can select…

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

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Q: Assume that a bakery has 7 different types of cakes. How many different ways can 5 cakes of any type…

A: We have total 7 cakes  From the 7 cakes, we have to pick a group of 5 cakes. So the arrangement does…

Q: Suppose we want to choose 6 colors, without replacement, from 9 distinct colors. (a) If the order of…

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Q: From a list of 50 captains, 4 are to be promoted to major. In how many ways can this be done? ways

A: It is provided that 4, r are to be promoted to major from a list of 50, n captains. As the order…

Q: There are 12 teams in a league. In how many ways can the teams finish first, second, third, and…

A: A permutation is a mathematical tool that helps us to find the number of possible arrangements in a…

Q: if 8 different colored beads are made into a necklace, how many necklaces can be produced having…

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Q: Suppose we want to choose 4 colors, without replacement, from 18 distinct colors. (If necessary,…

A: We have to find number of ways to choose.

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.