Identify the formula for the number of permutations when r objects are selected fromn objects. Choose the correct answer below. n! OA. nPr (r-n)! (r-n)! n! B. nPr= (n-r)! n! OC. Pr r(n-r)! n! . nPr= r!

Q: 1. If N = 12, k = 8, and n = 5. Find P(2). %3D

A: X follows a hypergeometric distribution with N=12, K=8 and n=5 and k=2 We will use the formula:…

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Q: Q1// Let Ai be even permutation in Sn. Then O(An)=n!/2

A: Even permutation:- element with even number of transportation belongs to even permutation set

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Q: IfΣ ( a+ bk) 4n_ and n+1 k-1 E(ar – br) +, then Ear n n+2 k=1 k-1 2 O None 2 2

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Q: 1) For each of the following scenarios, determine whether it is a permutation problem (order…

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Q: 3. If the following two permutations P, and P,r-1 are equal, solve for r.

A: Given that, 5Pr   and   6Pr-1 are equal. And we have to find the value of r.

Q: Use the permutation and combination formulas to prove the following. +k – 1) (n + k – 1 (b). V k, n…

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Q: (c) Show that a permutation o E S, commutes with r if and only if the permu- tation f(o) commutes…

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Q: Prove the following: P(n,r)=P(n-1,r)+r.,P(n-1,r-1)

A: Recall: P(n,r ) = Prn=n!(n-r)! n! = n(n-1)!

Q: 5) Find the total Ħ of díagonals for af )n=5 b)n=10

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Q: Choose the correct definition of from below. O A. kl(n- k)! n! O B. kl(k-n)! k! c. nl(n- K) O D. (n…

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Q: For what a is ||ai - 3j + k||=16

A: Topic - vectors

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Q: For any positive interger n, (n + 1)! / n! - n = (A) 0 (B) 1 (C) n (D) n + 1 (E) n!

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Q: 14. If n e Z, then 5n2 +3n + 7 is odd. (Try cases.)

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Q: 3) Show that 1-2+2-3+3-4+…+(n – 1) - n is O(n³). Also state the values for witnesses C and

A: Hi! You have posted multiple questions. As per norms, we will be solving only one question. We will…

Q: B. Express the following to fundamental principle of counting. 1. P3) 2. P (10,5) 3. P(4) 4. P() 5.…

A: we know that permutation formula = : P(n,r) = n! / (n-r)!

Q: O Prove thal P(m, n) - (n,m).

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Q: 2. Prove that n²>2n for n >2

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Q: ind the following permutations nPr. a. n = 9 and r = 4. b. n = 9 and r = 3. C. n 9 andr =

A: Find the following permutations   Formula to find permutations is nPr =n!(n-r)!

Q: (d) utive but no two X's can be consecutive? How many permutations are there, if all three of the…

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Q: prove the following P(n,r)=P(n-1,r)+r  ,P(n-1,r-1)

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Q: 3n-m Let C = n, m EN- Then sup(C) = n?m

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Q: 3. Use the permutation and combination formulas to prove the following. (a). For all integers n 2 3,…

A: Given n≥3, n€ Z (integer ) We have to prove that P(n, 3)+2P(n, 2)=nP(n, 2)

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Q: Find a formula for Sn, n > 1, if sn is given by 6 7 3' 5' 7' 9' 11 4 8 - Sn =

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Q: Show that the n-th tetrahedral number O_n is given by S_n= n(2n^2+1)/3

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Q: that d | n + 5 and d | n2 + 7, then d | 32. , then n + 5 and n2 + 7 are coprime.

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Q: Q1// Let Ai be even permutation in Sn. Then O(An)=n!/2 إضافة ملف

A: Question 1) Sn denotes the set of all permutations of n objects. Then, |Sn| = n! &amp;, An denotes…

Q: Suppose n e z. If n² is odd, then n is odd.

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Q: Pls help quick

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