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

Q: In the Superfecta, one must pick the first four finishers of a horse race in correct order. If there…

A: For this question, assuming that all the horses were alive after the race, i.e. there were no…

Q: To win at LOTTO in one​ state, one must correctly select 6 numbers from a collection of 63 numbers​…

A: Here, the order in which the selection is made does not matter.The possible selection is,

Q: San Pablo City is famous for its Seven Lakes namely: Sampaloc, Bunot, Yambo,  Pandin. Mohicap,…

A: Given that San Pablo City is famous for its Seven Lakes namely: Sampaloc, Bunot, Yambo, Pandin.…

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…

A:

Q: How many different letter arrangements can be made from the letters in the word of…

A: Given word is COMMUNICATION"c" is repeated 2 times"m" is repeated 2 times"N" is repeated 2 times"I"…

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: In how many ways can eight different DVDs be arranged on a shelf?

A: We need to arrange 8 DVDs

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

A:

Q: In how many ways can 7 beads can be arranged to form a necklace?

A: We have to arrange 7 beads in a circle so that we can form a necklace. Now we fix one bead and the…

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: 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: Find the smallest counting number n such that /n× 25200 is a counting number.

A: Find the smallest number n.

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

A: Given that there are ten books available to arrange them in shelf.

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

A:

Q: How many multiples of 6 are in the set {171, 172, 173, ..., 286}?

A: Given set is 171,172,173,174,.......,286. We have to find the number of multiple of 6 in the given…

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: answer the following questions using the appropriate counting techniques, which may be either…

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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?

A:

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: To win at LOTTO in one state, one must correctly select 7 numbers from a collection of 59 numbers (1…

A: From the provided information, Total numbers are from 1 to 59. To win at Lotto in one state one need…

Q: In how many ways can eight persons form a circle fora folk dance?

A:

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: Find the number of ways in which 9 different computer games can be shared out between Wainah, Jingyi…

A: Here there are 9 different computer games that can be shared between Wainah (W), Jingyi (J) and Hebe…

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

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Q: How many different numbers of five digits can be made using the digits 2,2,3,3,3?

A: The objective is to find how many different numbers of five digits can be made using the digits…

Q: In how many ways can 8 different pizza toppings be chosen from 14 available toppings? There are ways…

A:

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: 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: How many 5-digit license plate numbers can we generate from the numbers, 0, 1, 2, 3, and 4 if it…

A: Given: There are 5digits 0 , 1 , 2 , 3 , 4 We need to count number of  5 digit number plates…

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

A: Introduction: Suppose there are n items to be arranged among themselves. Further, consider there are…

Q: A photographer is asked to submit seven photographs from a collection of 14 for an exhibit. In how…

A:

Q: To win at LOTTO in one​ state, one must correctly select 7 numbers from a collection of 45 numbers​…

A: Given, Total collection of numbers = 45 numbers​ and, The order in which the selection is made does…

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

A: According to the principle, if there are n objects with r1 objects of one kind, r2 objects of…

Q: How many multiples of 11 are in the set {1, 2, 3, .., 901}?

A: To find the number of multiples of 11 are in the set {1, 2, 3, ..., 901}, we use the following…

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: If 20 paintings are entered in an art exhibit, in how many different ways can the judges award a…

A: It is given that, 20 paintings are entered in an art exhibit. Then judge award the first prize to…

Q: Create a Fundamental Counting Principle problem and determine the number of ways it can be…

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

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Q: Given 9 digits,   1,23,4,5,6,7,8,9, how many 3-digit numbers could be formed without repetition of…

A: Given ,total no.of digits=9 (1 to 9)

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: In how many ways can 16 different pizza toppings be chosen from 20 available toppings? There are…

A:

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

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.