Consider the following permutations in S,: 3 4 5 6 7 2 3 4 5 B- 3 2 75 1 6 !! 7 5 4 1 3 their product Ba is O 236547) O None of these O ( 236574) O (236457)

Q: 7. Prove without using induction that is a is an odd integer, then a? – 1 is divisible by 8.

A: We use the fact that every odd integers are of the form 2n+1 for some n belongs to integers.

Q: It the n objects in a permutations problem are not all distingushable-hat is, 4 there are n, of type…

A: Solution: From the given information, the word is KANSAS.

Q: Let A and (A, n2 1) be subsets of 2 An - A as n → 00 =P(A,) P(A). as n 0o,

A: The given question is related with probability. Given that A and An , n≥1 are subsets of Ω . We have…

Q: Show that C(p,1), C(p,2),..., C(p,p-1) are all divisible by p if and only if p is a prime.

A: As per the question we have to prove that C(p,1), C(p,2),..., C(p,p-1) are all divisible by p if and…

Q: (123456 Let o = find o25 314562 ect one: 123456 612 435) (123456 124365 (123456 314562 (123456…

A:

Q: Consider the following permutations in S,: (1 2 3 4 5 6 7) a = 6 2 7 1 4 5 3) their product aß is (1…

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Q: An integer n > 2 is composite if and only if n does not divide (n - 1)! + 1. :Select one True False

A: The solution is given as

Q: (1234 56 314562, Let o = find o5 (1234 56 314562, (1234 56) 612435, O None of them 1234 56) (124365…

A: Just write the given permutation in cycle form and then compute the order of permutation and you'll…

Q: Find the number of 4-permutations of a set of 9 objects. (select the correct answer) ○ 162 ○ 126 ○…

A: Step 1:To find the number of 4-permutations of a set of 9 objects, the following formula can be…

Q: If an n-cycle o e S, is a product of an even number of transpositions then o is called an even…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Let a = (17 3)(5 9 4 2) and B = (2 3)(7 4)(5 18) be elements of S10. Then, a’B is O (1 4)( 2 7 5 3 9…

A:

Q: Show that a permutation may only be created by a stack (as in the previous question) if it does not…

A: To prove that a permutation cannot be created by a stack if it contains a banned triple  with c…

Q: 5. Let p = 61. Find all incongruent elements modulo 61, that have order: (а) 5 (b) 10 (с) 60

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Q: Which of the following is equal to 0 0 0 0 0 10 П 10! 4! 10! - 4! 10! (1!+ 2! +3!) 10! 3! 10! 3! 10!…

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Q: 2. Make a conjecture about the sum of primes based on the following pattern: 4= 2+2 6=3+3 8=3+5…

A: Given:4=2+26=3+38=3+510=3+712=5+7and so on...

Q: 5 a Prove the following statements If n be an integer such than n² is even, then n² is div

A: We use definition of divisibility. And we use general form of any integer.

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

A: Solution :-

Q: Consider the following permutations in S,: (1 2 3 4 5 6 7 4 5 6 7 7 1 5 6) 1 3 a = 6 2 7 their…

A: To find the product of given permutations

Q: Let denote the binomial coefficient (also written as C(n, r) or nCr). The sum of (C) + (4) +…

A:

Q: Use the factorization A = PDP 21-2²: 15 -42 4 -11 AK = 0 37 10 I k to compute A^, where k represents…

A: Given information:To find:Use the factorization to compute , where  represents an arbitrary…

Q: 12 765,986 = 6 (mod 10) Select one: O True O False

A:

Q: A computer password is to consist of five alphanumeric characters with no repeats. (An alphanumeric…

A: We have given that A computer password is to consist of five alphanumeric characters with no…

Q: Let ? and ? be permutations on the set {1,2,3,4,5,6,78,9}, defined as follows

A: Introduction: A permutation is a bijective mapping from a set to itself. The general way to…

Q: Given a positive integer n, how many strings of n letters from the English alphabet (26 letters)…

A: English alphabets vowels are A,E,I,O,U and rest 21 are consonants

Q: Question * Consider the following permutations in S;: (1 2 3 4 5 6 7) a = 6 2 7 1 4 5 3) B - ; (1 2…

A:

Q: The number of permutations of a set of n elements is     set in a specific order     arrangement…

A: The number of permutations of a set of n elements is     set in a specific order…

Q: Find how Many 9-digit numbers can be Made from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 if repetition is…

A:

Q: Consider the following permutation in Sg, 12 3 4 5 6 7 8 9 3 7 2 5 49 618 1ttt t tt (a) Write this…

A:

Q: Consider the following permutations in S7: (1 2 3 4 5 6 7) "- (6 2 7 5 4 1 3) The order of ß is (1 2…

A: Consider the given permutations  α and β. We need to find the order of  β. The solution is given…

Q: Which of the following consists of 6 consec- utive composite numbers 2,3,5,7,9,11 7071, 7072, 7073,…

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Q: 4. Count the permutations 111213141516 of 1, 2, 3, 4, 5, 6} where i • 12 #1 i3 #1 1,2,3 i5 5,6 i6 #…

A: count the permutations  i1,i2,i3 i4,i5,i6 of  1,2,3,4,5,6 where i1≠1,2,3 i2≠1 i3≠1 i5≠5,6 i6≠5,6

Q: 1. Which of the following permutations in S, is odd? (a) 53124 (b) 51423 (c) 51234 (d) 54231

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Q: 100! .. .(mod103) (a 60 (b) 50 (c) 51 (d) None of these

A:

Q: w+1 (a) Rewrite 3 2 n(n – 1) with the change of variable m = n+2. n=0

A: a) The given expression 3∑n=0w+1nn-1m=n+2n=m-2