A classic counting problem is to determine the number of different ways that the letters of "balloon" can be arranged. Find that number.

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

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Q: in how many ways can 5 children be arranged in a line for a photograph?

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Q: In how many ways can 4 pizza toppings be chosen from 12 available toppings? Your answer is:

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Q: It is desired to write a 3-digit number using the numbers 2, 3, 4, 5, 6, 7, 8. If each number is…

A: Given data: The total numbers are n=7. Case-1 The total 3 digits numbers that can be formed from the…

Q: A license plate must contain 2 numerical digits followed by 2 letters. If the first digit cannot be…

A: Given 1. A license plate must contain 2 numerical digits followed by 2 letters. 2. the first digit…

Q: Ms. Ling has 16 boys and 14 girls in her third-grade class. How many ways can she select 2 boys or 2…

A: Ms. Ling has 16 boys and 14 girls in her third-grade class. We want to find how many ways can she…

Q: Four members from a 14 members committee are to be randomly selected to serve as a Chair, a…

A: The number of members is 14.

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: We can use the fundamental counting principle to count the number of possible 4 digit ATM PIN…

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Q: A lottery game called Quinto is played by choosing five numbers each, from 0 through 9. How many…

A: You didn't tell us whether order mattered Here, repeats are allowed If order mattered The answer is…

Q: to win a lotto in one state, one must correctly select 6 numbers from a collection of 5 numbers (one…

A: In the question, it has to be select 6 numbers from a collection of 55 numbers (one through 55),…

Q: Several states participate in Hot Lotto, a lottery that requires choosing 5 of the numbers 1-39 and…

A: It is given that lottery  requires choosing 5 of the numbers 1 to 39. Substitute n=39,r=5 in…

Q: A photographer is asked to submit 7 photos from a collection of 14. How many ways can the photos be…

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Q: How many different 5-digit phone numbers do not contain the digit 6? Assume that any digit in the…

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Q: Suppose there are 5 questions in an exam paper, find the number of ways in which a student can…

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Q: In how many ways can eight children posing for a photograph line up in a row?

A: 8! = 40320 ways can eight children posing for a photograph line up in a row

Q: How many 4-digit numbers are there?   And if repetition of digits is not allowed?

A: Given that n= number from 1 to 9 = 9 r = 4 ( since we have to take 4 digit number)

Q: Assume that four men and four women are to sit in a row of eight chairs. In how many ways can these…

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Q: Find the number of different ways that a family of 9 can be seated around a circular table with 9…

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Q: to win at lotto in one state, one must correctly select 6 numbers from a collection of 63 numbers?

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Q: What is the smallest multiple left out of this cluster of 12, 18,9,3 and 15

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Q: A classic counting problem is to determine the number of different ways that the letters of…

A: The number of different ways to arrange a word:Consider the total number of letters in a word be…

Q: How many different 7-digit phone numbers can have the digits 7,3,5,2,7,3 and 2?

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Q: A bag contains 15 pieces of candy. In how many ways can four pieces be selected?

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Q: How many ways are there to select 47 cards from a standard deck of 52 cards?

A: To find: The number of ways to select 47 cards from a standard deck of 52 cards. Concept used: The…

Q: In how many different ways can six books be arranged on a shelf?

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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: Suppose that a bake shop Has four different kinds of cookies. How many different ways can six…

A: We are choosing 6 cookies, i.e r = 6 and  we need 4 different kinds of cookies, i.e n= 4

Q: How many different five letter “words” can be made out of the letters in the word world?

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Q: Answer the following question using the appropriate counting​ technique, which may be either…

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Q: In how many ways can 5 sets of numbers be picked from 50 numbers in a lottery?

A: From the provided information, Total numbers in a lottery = 50 The required number of ways of…

Q: How many seven-digit numbers can be made from the digits 1 to 9 if repetition is allowed?

A: Given that  To find the number of ways of 7 digit number can be made from the 1 to 9

Q: Assume that five men and five women are to sit in a row of ten chairs. In how many ways can these…

A: If all men must sit together and all the women must sit​ together then, either the men can take the…

Q: From 9 names on a ballot, a committee of 5 will be elected to attend a political national…

A: Determine the number of different committees is possible. Combination: A combination is a selection…

Q: Find the permutation. From 1650 raffle entries, five entries will be chosen for first, second,…

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Q: Assume that three men and three women are to sit in a row of six chairs. In how many ways can…

A: Let's find.

Q: It is desired to write a 3-digit number using the numbers 2, 3, 4, 5, 6, 7, 8. If each number is…

A: If the 3 digited number is greater than 300, then it will start with the numbers 3, 4, 5, 6, 7, 8.…

Q: Assume that four men and four women are to sit in a row of eight chairs. In how many ways can…

A: There are two ways to sit for four men and four women in a row of 8 chairs.

Q: Determine the numbers of ways to deal 13 cards on the table having aces of diamonds and clubs from a…

A: GivenNo.of cards to deal on the table =13No.of Ace of diamond cards = 1No.of Ace of club cards = 1

Q: A classic counting problem is to determine the number of different ways that the letters of…

A: The letter Recommend can be arranged  Total no of letters = 9 e is repeated 2 times m is repeated 2…

Q: A hotel reservation number consists of 5 digits, followed by 2 letters, followed by 2 digits. How…

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Q: How many ways can 9 different Geometry books be stacked on a shelf?

A: The given question is a multiple question, so as per the rule, we are doing only first question:…

Q: Do we know if the number of primes is finite

A: No, the number of primes is not finite because whatever the list of prime number exist, is…

Q: Based on each given problem, draw a tree diagram in the space provided. Then, use the Fundamental…

A: Given: The work "MAT". To find: Number of arrangements of 3 letters in the word "MAT".

Q: How many different ID cards can be made if you must choose 7 digits followed by 2 letters and any…

A: There are 10 digits  0,1,2,3,4,5,6,7,8,9 There are 26 alphabets A,B,C,D..... Z

Q: In how many ways can 12 books be divided among 4 students so that each student receive three books?

A: Given that : Total books (n) = 12 Divided among 4 student and each student get books = 12/ 4  = 3 So…

Q: This problem involves combinations. In how many ways can ten people be chosen from a group of…

A: Problem related to permutations and combinations

Q: To win at LOTTO in one​ state, one must correctly select 7 numbers from a collection of 49 numbers​…

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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.