How many ways are there that no two students will have the same birth date in a class of size 60?

Q: How many ways can we arrange eleven bowling balls numbered 1 to 11 in a circle if the even- numbered…

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Q: Explain the difference between a permutation and a combination of n items taken r at a time.

A: Two types of counting problems occur so frequently that they deserve specialattention. These…

Q: In how many ways can first, second, and third prizes be awarded in a contest with 875 contestants?…

A: Given information- We have given that in a contest 875 contestants participated. We have to give…

Q: In how many different ways can the letters in "restlessness" be arranged?

A: From the provided information, The total letters in word “restlessness” are 12. The letters are…

Q: If you toss 10 fair coins,in how many ways can you obtain at least one head?

A: Given: 10 fair coins are tossed. We want to calculate the number of ways in which we can obtain at…

Q: A brand of jeans comes in nine different washes, five different fit styles, and three different…

A: Given that there are: 9 different washes, 5 different fit styles, 3 different height options.   2 of…

Q: In how many ways can a student choose to do 7 questions out of 8 on a test?

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Q: In how many ways can an adviser assign a different task to 9 students from a class of 15?

A: Here we need to assign a different task then we would use combination.   Combination formula: C(n,r)…

Q: In how many ways can a class of 32 students select four people to serve on a committee?

A: Total number of students in the class (n) = 32 Number of students to be selected to serve on a…

Q: how can the children in ms. varner's class tell if there is an even or odd number of children in the…

A: The children's are :

Q: A committee of four people is to be chosen from a nine member group to represent the group on an…

A: No of combinations of n objects takes r at a time isncr=n!n-r!r!Similarly here 4 members to be…

Q: In how many ways can 10 people be seated in 10 adjacent seats in a theater?

A: Given: In how many ways can 10 people be seated in 10 adjacent seats in a theater. We need to…

Q: In how many ways can 5 persons be seated in a room where there are 10 seats?

A: We have to find number of ways to seat people in room.

Q: In how many different ways can eight people be seated in a row?

A: Different ways that eight people can sit in a row.

Q: A School's working day is divided into six periods. How many different ways may five subjects be…

A: From the provided information,   5 subjects can be arranged in a 6 periods in P56 ways. Any of 5…

Q: If 15 people start a race, in how many different ways can the top 3 finishers be determined?

A: Permutation:   It  is an arrangement of objects in a definite order where the order is important.…

Q: In how many ways can 6 different cupcakes be arranged in a circular stand?

A: The number of ways n items can be arranged in a circle is equal to n-1!. The formula for n! is…

Q: How many ways are there to win first, second, and third places in a rally with 14 cars, provided…

A: The number of cars in the rally is 14. The first place can be chosen in 14 ways. Since one car has…

Q: There are four balls of different colors. Two balls at a time are taken and arranged any way. How…

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Q: Out of 6 children, in how many ways can a family have at least 1 girl?

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Q: How many ways can 7 out of 15 patients with the same illness be randomly selected to receive an…

A: The question is asking for the number of ways to choose 7 patients out of 15. This is a problem of…

Q: How many permutations can be made out of the letters in the word CAROLINE taken 4 at a time?

A: There are 8 letters in the word CAROLINE. We can take 4 letters from 8 letters in 8P4=8!(8-4)!=1680…

Q: In how many different ways can we arrange 10 experimental hamsters in 10 laboratory cages if 4…

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Q: In how many ways can we select seven cases of beer from three brands if order does not matter?

A: = 36Explanation:To solve this problem, we need to use the concept of combinations. Given…

Q: In how many ways can we arrange the letters in the word T

A: Given word is "TOOTH". The letters are T, O, O, T, H. The number of letters is 5. And the letter "O"…

Q: If 10 people come from different places and shake hands in how many different way could this be done

A: The formula for the number of handshakes possible with n people is          handshakes = n*(n -…

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 bag of three identical balls and four identical coins be formed from a group…

A: Given: Total number balls =12 Total number coins =12

Q: In how many ways can nature select 4 students out of a class of 15 students to get the flu? In how…

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Q: A race is being run by ten horses. How many distinct permutations of first, second, and third place…

A: Let n be the number of horses run in a race. i.e. n=10 and r be the number of places to be awarded.…

Q: In how many ways can the judges in the Miss USA pageant choose the American representatives to the…

A: The number of ways can the judges in the Miss USA pageant choose the American representatives to the…

Q: Question 1 In how many ways a captain can be made in a class having 3 boys and 4 girls?

A: 3 boys and 4 girls in class  we have to find no. of ways to choose captain = ?

Q: How many different arrangements can b

A: Given the word          "SIPNAYAN"

Q: A new smartphone comes in five colors, two screen sizes, and four different data plans.  In how many…

A: It is given that a new smartphone comes in five colors, two screen sizes, and four different data…

Q: Different amounts of money can be made from 5 coins of different denominations. Find the probablity…

A: Total number of amounts of money that can be made with 5 coins =C15+C25+C35+C45+C55 =31