2. Let Qn be the number of permutations of {1,2, .., n} in which none of the patterns 12, 23, .., (n – 1)n оссurs. ) Find Q3 by listing all the possible permutations. ) Use the inclusion-exclusion principle to prove that (a) { (b) (- - n - 2 + 2! (-1)"-1 (п — 1)! n – 1 п - 3 Qn = (n – 1)! (n- 1! 3!

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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2. Let Qn be the number of permutations of {1,2,..., n} in which none of the patterns 12, 23, .., (n – 1)n
.....
occurs.
) Find Q3 by listing all the possible permutations.
) Use the inclusion-exclusion principle to prove that
(a) {-
(b)
(-1)"-1
(n – 1)!
n - 1
п — 2
n – 3
Qn = (n – 1)! ( n
+...+
3!
1!
2!
Transcribed Image Text:2. Let Qn be the number of permutations of {1,2,..., n} in which none of the patterns 12, 23, .., (n – 1)n ..... occurs. ) Find Q3 by listing all the possible permutations. ) Use the inclusion-exclusion principle to prove that (a) {- (b) (-1)"-1 (n – 1)! n - 1 п — 2 n – 3 Qn = (n – 1)! ( n +...+ 3! 1! 2!
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