How many permutations of {1,2,3,4,5,6,7,8} have exactly 15 inversions?

Q: How many permutations of a set five distinct objects taken three at a time are there?

A: Given:-                 How many permutations of a set five distinct objects taken three at a time…

Q: Suppose we select 3 students randomly out of a class of 10 students to read a  paper from the…

A: Combination:   It is nothing but the objects are being selected when the order of selection is not…

Q: In how many ways can 2 children and 5 adults be seated in a row of the children must be seated at…

A: Given information: 7 people consisting of 2 children and 5 adults, are to be seated in a row.  It…

Q: Assume the cards are drawn sequentially and without replacement. (permutations) In how many ways…

A: Given data, given that 5 Spades can be drawn from a standard deck of 52 cards. The cards are drawn…

Q: How many ways are there to arrange 12 identical apples and five different oranges in a row so that…

A: Here, arrange 12 identical apples and five different oranges in a row so that no two oranges will…

Q: How many permutations of the 26 letters in the English alphabet contain the string abc and end on…

A: We have to find the number of permutations.

Q: You are among 12 people forming a chess club.​ Collectively, you decide to put each​ person's name…

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Q: How many permutation can we make if we have 12 elements and use 4 at a time?

A: Given data:   The total numbers of elements are n=12. The numbers of elements used at a time are…

Q: Nine persons enter a lift from ground floor of a building which stops in 10 floors (excluding ground…

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Q: 5. How many 2-permutations are there of a set of eight objects?

A: We know that,  The formula pf permutations is,  nPr = P(n, r) = n!/(n-r)!

Q: How many permutations π of [10] satisfy π^5 = 1?

A: The given set is 10=1,2,3,…,10. Therefore any permutation π of 10, is bijective function from the…

Q: (a) How many 3 digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9 which are divisible…

A: As we want our 3-digit number to be divisible by 5, the number 5 will be fixed on the unit's place…

Q: 7) Suppose that a class of 20 students is assigned to write an essay. Suppose 4 essays are picked at…

A: Total number of students in class = 20 Number of essays to be picked at random = 4

Q: . Five-digit-numbers can be formed from the six digits 2, 3, 5, 6, 7 and 0. If repetitions are not…

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Q: XI In a group of 11 boys and 9 girls, 5 are to be selected. In how many ways can they be selected…

A: According to the answering guidelines, we can answer only one question at a time and the rest can be…

Q: Give the transpose of the permutation [2, 5, 1, 6, 3, 4], and find the number of inversions in both…

A: To find- Give the transpose of the permutation 2, 5, 1, 6, 3, 4, and find the number of inversions…

Q: In how many ways can a committee of 5 be formed from 5 juniors, and 7 seniors, if the committee must…

A:

Q: Is a permutation of one element considered to be an even permutation? For example, is (1) an even…

A: To clarify the notion of an even permutation

Q: How many different permutations each containing all letters of the word STATESMAN can be formed 2 -…

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Q: A musician plans to perform 5 selections. In how many ways can she arrange the musical selections?…

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Q: How many different ways can you arrange 2 letters from a set of 3 letters {T, S, U} such that…

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Q: In how many ways can they line up so that no two geese are standing next to one another? (There is…

A: There are 10 ducks and 6 geese.

Q: How many inversions are in the following permutation?: [2, 5, 1, 6, 3, 4]

A: Inversions of a permutation

Q: How many permutations of [n] are possible in which no even numbers and no odd numbers are adjacent?

A: Solution :-

Q: How many permutations of {1,2,3,4,5,6,7} have exactly one element fixed?

A: Using inclusion-exclusion principle to compute the given permutation: There are 71·6! ways to select…

Q: Solve the following set of combinations and permutations.   How many two digit numbers can be…

A: 1)From the provided information the four digits are 1,2,3,4, so the first digit can be any of these…

Q: How many distinct permutations can be made from the letters of the word "COMBINATORICS" ?

A: Given word is: "COMBINATORICS" Total number of letters are 13. Multiplicity of letter C is 2.…

Q: 4. How many permutations are there of the letters in the word BALLOON if the first and the last…

A: (As per bartleby guideline for more than one question asked, Only one will be solved, Please upload…

Q: How many different ways can you arrange 2 letters from a set of 3 letters {L, S, U} such that…

A: There are 3 distinct letters. We must find the number of ways 2 of these letters can be arranged…

Q: 16. A soccer team has 11 players on the field at the end of a scoreless game. According to league…

A: Solution

Q: How many 6-permutations of [15] have their digits in increasing order?

A: Permutation is a technique to obtain the possible arrangements of listed items in a linear order.…

Q: A restaurant offers a special pizza with any 5 toppings. If the restaurant has 10 topping from which…

A: this is a combination problemtotal number of topping=10number of topping can be chosen=5so number of…

Q: Find the number of distinguishable permutations of: 5 As, 3 Gs, and 4 Ns

A: The answer is, 27720   The detailed solution is as follows below:

Q: Jack is playing with a standard deck of 52 playing cards. He shuffles the cards and then turns the…

A:

Q: Given the permutation, [2, 5, 1, 6, 3, 4], and its transpose, [4, 3, 6, 1, 5, 2], find the number of…

A: The given permutation is: 2,5,1,6,3,4 Its transpose is: 4,3,6,1,5,2

Q: Number of circular permutations of different .!things taken all at a time is (n-1)

A:

Q: How many permutations are there of the letters in the word 'PENCILS', if all the letters are used…

A: If all the letters in the word are distinct and we have to arrange letters without repetition, then…

Q: 1. A registration code begins with three numbers. If the possible numbers are 1, 2, 7, 9 and 0, how…

A: We have find on of more..

Q: (a) How many permutations of (10] are there that EITHER alternate even and odd numbers or have even…

A: Let consider the permutations of 10 as the ordering of  the elements of 10 rather than as an…

Q: In how many ways can 4 t-shirts, 7 denims, and 4 coats be arranged in a clothing store shelf section…

A:

Q: How many 5-number license plates can be made using the digits 1,2,3,4,5,6,7, if an odd digit must…

A: Given Data: The total number of digits available is: n=7 The numbers required on number plate is:…

Q: How many numbers lying between 100 and 1000 can be formed with the digits 0, 1, 2, 3, 4, 5 if the…

A: Total numbers 0 , 1 , 2 , 3 , 4  5 = 6

Q: How many permutations of {1, 2, 3, 4, 5, 6, 7} leave exactly 1 element fixed?

A:

Q: How many permutations are there of the letters in the word 'CHARGES', if all the letters are used…

A: The formula for Permutation is nPr = n!/(n – r)!.

Q: many permutations can be formed with two types of objects with n objects of type 1 and n^2 objects…

A:

Q: 2.21 Registrants at a large convention are offered 6 sightseeing tours on each of 3 days. In how…

A: Given: Number of sight seeing offered=6 Number of days of tour=3 Determine the number of ways in…

Q: How many six-number combinations can be generated from the numbers from 1 to 42 inclusive, without…

A: Given information: A 6 number combination is to be generated. The possible numbers are selected…

Q: How many permutations of the 26 letters (English alphabet) do not contain any of the strings zero,…

A: Total number of permutations of 26 letters  (N) = 26! Number of permutations in which ZERO always…

Q: 1.How many different four-letter passwords can be formed from the letters A, B, C, D, E, F and G if…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: How many permutations of {1, 2, 3, 4, 5, 6, 7, 8) leave exactly 1 element fixed?

A: