Prove that: n! (n + 2) = n! + (n + 1)!
[6] Permutations and Combinations
Chapter: [6] Permutations and Combinations
Concept: undefined >> undefined
If (n + 2)! = 60 [(n − 1)!], find n.
[6] Permutations and Combinations
Chapter: [6] Permutations and Combinations
Concept: undefined >> undefined
If (n + 1)! = 90 [(n − 1)!], find n.
[6] Permutations and Combinations
Chapter: [6] Permutations and Combinations
Concept: undefined >> undefined
If (n + 3)! = 56 [(n + 1)!], find n.
[6] Permutations and Combinations
Chapter: [6] Permutations and Combinations
Concept: undefined >> undefined
If \[\frac{(2n)!}{3! (2n - 3)!}\] and \[\frac{n!}{2! (n - 2)!}\] are in the ratio 44 : 3, find n.
[6] Permutations and Combinations
Chapter: [6] Permutations and Combinations
Concept: undefined >> undefined
Prove that:
\[\frac{n!}{(n - r)!}\] = n (n − 1) (n − 2) ... (n − (r − 1))
[6] Permutations and Combinations
Chapter: [6] Permutations and Combinations
Concept: undefined >> undefined
Prove that:
\[\frac{n!}{(n - r)! r!} + \frac{n!}{(n - r + 1)! (r - 1)!} = \frac{(n + 1)!}{r! (n - r + 1)!}\]
[6] Permutations and Combinations
Chapter: [6] Permutations and Combinations
Concept: undefined >> undefined
Prove that:
\[\frac{(2n + 1)!}{n!}\] = 2n [1 · 3 · 5 ... (2n − 1) (2n + 1)]
[6] Permutations and Combinations
Chapter: [6] Permutations and Combinations
Concept: undefined >> undefined
If P (5, r) = P (6, r − 1), find r ?
[6] Permutations and Combinations
Chapter: [6] Permutations and Combinations
Concept: undefined >> undefined
If 5 P(4, n) = 6. P (5, n − 1), find n ?
[6] Permutations and Combinations
Chapter: [6] Permutations and Combinations
Concept: undefined >> undefined
If P (n, 5) = 20. P(n, 3), find n ?
[6] Permutations and Combinations
Chapter: [6] Permutations and Combinations
Concept: undefined >> undefined
If nP4 = 360, find the value of n.
[6] Permutations and Combinations
Chapter: [6] Permutations and Combinations
Concept: undefined >> undefined
If P (9, r) = 3024, find r.
[6] Permutations and Combinations
Chapter: [6] Permutations and Combinations
Concept: undefined >> undefined
If P(11, r) = P (12, r − 1) find r.
[6] Permutations and Combinations
Chapter: [6] Permutations and Combinations
Concept: undefined >> undefined
If P (n, 4) = 12 . P (n, 2), find n.
[6] Permutations and Combinations
Chapter: [6] Permutations and Combinations
Concept: undefined >> undefined
If P (n − 1, 3) : P (n, 4) = 1 : 9, find n.
[6] Permutations and Combinations
Chapter: [6] Permutations and Combinations
Concept: undefined >> undefined
If P (2n − 1, n) : P (2n + 1, n − 1) = 22 : 7 find n.
[6] Permutations and Combinations
Chapter: [6] Permutations and Combinations
Concept: undefined >> undefined
If P (n, 5) : P (n, 3) = 2 : 1, find n.
[6] Permutations and Combinations
Chapter: [6] Permutations and Combinations
Concept: undefined >> undefined
Prove that:1 . P (1, 1) + 2 . P (2, 2) + 3 . P (3, 3) + ... + n . P (n, n) = P (n + 1, n + 1) − 1.
[6] Permutations and Combinations
Chapter: [6] Permutations and Combinations
Concept: undefined >> undefined
If P (15, r − 1) : P (16, r − 2) = 3 : 4, find r.
[6] Permutations and Combinations
Chapter: [6] Permutations and Combinations
Concept: undefined >> undefined
