Find the number of permutations x1, x2, x3, x4, x5,  of numbers 1, 2, 3, 4, 5 such that the sum of five products  x1x2x3 + x2x3x4 + x3x4x5 + x4x5x1 + x5x1x2 is divisble by 3

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: Compute P5,2.

A: The ordered combination is known as permutation. It is denoted by P(n,r) Where n is the number of…

Q: Prove that Master Cheng has won precisely 21 times in a row during some consecutive days.

A: Please find the solution

Q: Compute the sum of the first 60 positive integers that are exactly divisible by 4.

A: The numbers divisible by 4 is:

Q: 8) а, %3-31104 and a, = -4 %3D А) -5, —30, —-180, —1080, —6480 В) -6, —36, —-216, -1296, —7776 С) 4,…

A: Use the nth term of an gp for finding the rest terms

Q: Find all three-digit numbers with different digits with the property that those numbers are…

A: Given that it is to be found all three-digit numbers with different digits with the property that…

Q: Find all the mindir and colartors of matrin A. -2 3. A- 6. -1 -3 1.

A: The minor of all the elements of a matrix can be obtained by deleting the corresponding row and…

Q: Suppose a set of 8 numbers are selected from the set: {1,2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}…

A:

Q: A baseball team has 5 left-handed and 12 right-handed hitters and 3 switch hitters (either left or…

A:

Q: How many permutations of the numbers (1, 2, 3, 4, 5, 6, 7, 8, 9} have the numbers 4, 5 and 6 in…

A: So, the numbers 4, 5 & 6 should remain at their natural position and the other numbers can…

Q: 2. In how many ways can three numbers be selected from the numbers 1, 2, ... , 300 such that their…

A: This problem is solved using the concept of permutation and combination. please find step by step…

Q: Express the permutation (2 4 5)(1 3 5 5)(1 25) as a single cycle or as a product of cycles.

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: If a small monster collector has 20 small monster containment devices; intends to use all of those…

A: The small monster collector has containment devices and will use all of them, while capturing at…

Q: How many pairs of two distinct integers chosen from the set {1, 2, 3,..., 101} have a sum that is…

A: Since you have posted multiple questions and we can answer one question. So answer provided for the…

Q: A 3 × 7 rectangle is divided into 21 squares each of which is colored red or black. Prove that the…

A: Solution: let suppose the board is a 3 × 7 rectangle.

Q: How many 4-permutations of the multiset {A®, B®,C5,D²} exist?

A: claim- how many 4-permutation of the multiset A∞ , B∞ , C5 , D2exist ? as we know  number of r…

Q: Assume that product codes are formed from the letters X, T, and R, and consist of 6 not necessarily…

A: Given,  Product codes are formed from the letters X, T, and R, and consist of 6 not necessarily…

Q: Show that if seven integers are selected from {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, there must be…

A:

Q: 17. Show that Z () = zlog

A: Z-tramsform

Q: Compute P5,2

A: Permutation:          The act of arranging the members of a set into an order or sequence, if it is…

Q: Suppose any possible arrangement of 8 letters is considered a word and the letters are chosen from…

A:

Q: A 4-sided die with numbers 1, 2, 3, 4 on the faces, is rolled n times in row, and the numbers that…

A:

Q: Find the number of permutations without replacement that can be created by drawing 5 balls from a…

A:

Q: Compute C7,2

A: From the provided information, Expression is as follow: 7C2

Q: Suppose 7 female and 6 male applicants have been successfully screened for 5 positions. In how many…

A: Given ,no.of females =7no.of males =6Total no.of peoples=13

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: Find the set of all positive integers n with the property that the set  M={n,n+1,n+2,n+3,n+4,n+5}…

A: A very good problem based on a nice application of quadratic residues

Q: Show that there are infinitely many examples of two consecutive positive integers that cannot be…

A: According to the given information, It is required to prove that there are infinitely many examples…

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: A product code consists of a string of 4 different letters selected from the set {S,T,U,V,W,X}. How…

A: The number of ways to arrange r objects selected from n distinct objects is given by the permutation…

Q: A group of 12 environmentalists comprising of 7 lecturers and 5 technicians are to be selected to…

A: In the question , we are given the following information :  Total number of people =  12  Number of…

Q: | Suppose 10 ducks and 6 geese line up in a single row. In how many ways can they line up so that no…

A:

Q: please do 5

A: (a) Use the Euclidean algorithm to find the GCD as follows.

Q: find all three-digit number with different digits with the property that those numbers are divisible…

A:

Q: Suppose each license plate in a certain state has three digits followed by three letters. The digits…

A:

Q: How many distinct permutations can be formed from all letters of the word “SOCIOLOGICAL”? Moreover,…

A: Consider the given word SOCIOLOGICAL. The total number of letters is 12 N=12. Out of these, there…

Q: Bayes' rule can be used to identify and filter spam emails and text messages.In this collection, 747…

A: Given DataP(Spam) = 0.1340P(Not spam) = 1- P(spam) = 1 - 0.1340 = 0.866P(Free) = 0.0475P(Free and…

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: How many ways are there to permute the elements of the multiset {1,1,2,2,3,4,5,6} so the first and…

A:

Q: A technology company is going to issue new ID codes to its employees. Each code will have two…

A:

Q: Show that if any 14 numbers are selected from the set S = {1,2,3,...,25}, [14] there are at least…

A: Note that the numbers in each of the first twelve sets sum to 26, and that there is no pair of…

Q: Suppose each license plate in a certain state has four letters followed by two digits. The letters…

A: There are 6 positions in the license plate that need to be filled. Out of these 6, first 4 positions…

Q: Suppose that there are n = 2k teams in an eliminationtournament, where there are n∕2 games in the…

A:

Q: Let [A1, A2], [B1, B2], [C1, C2] be 3 married couples who attended a concert.  Show that the number…

A: Consider that G is the group of females and B is the group of males.This two group of G and B can be…

Q: An oil company is going to issue new ID codes to its employees. Each code will have one letter,…

A:

Q: There are 9 cards each written with the numbers 1, 2, 2, 3, 3, 3, 4, 5 and 6. Cards with odd numbers…

A:

Q: Find three subsets of {1, 2, 3, 4, 5, 6, 7, 8, 9} such that the intersection of any two has size 2…

A: Explanation of the answer is as follows

Q: Suppose each license plate in a certain state has four letters followed by two digits. The letters…

A:

Q: Find the number of ways 66 identical coins can be separated into three nonempty piles so that there…

A: GivenTotal number of identical coins =66Total number of piles =3 Each pile is on empty and the…

Q: Suppose each license plate in a certain state has one digit, followed by four letters, followed by…

A: Given, Each license plate in a certain state has one digit followed by four letters followed by one…