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Prove that:
\[\frac{n!}{(n - r)! r!} + \frac{n!}{(n - r + 1)! (r - 1)!} = \frac{(n + 1)!}{r! (n - r + 1)!}\]
Concept: undefined >> undefined
Prove that:
Concept: undefined >> undefined
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If P (5, r) = P (6, r − 1), find r ?
Concept: undefined >> undefined
If 5 P(4, n) = 6. P (5, n − 1), find n ?
Concept: undefined >> undefined
If P (n, 5) = 20. P(n, 3), find n ?
Concept: undefined >> undefined
If nP4 = 360, find the value of n.
Concept: undefined >> undefined
If P (9, r) = 3024, find r.
Concept: undefined >> undefined
If P(11, r) = P (12, r − 1) find r.
Concept: undefined >> undefined
If P (n, 4) = 12 . P (n, 2), find n.
Concept: undefined >> undefined
If P (n − 1, 3) : P (n, 4) = 1 : 9, find n.
Concept: undefined >> undefined
If P (2n − 1, n) : P (2n + 1, n − 1) = 22 : 7 find n.
Concept: undefined >> undefined
If P (n, 5) : P (n, 3) = 2 : 1, find n.
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.
Concept: undefined >> undefined
If P (15, r − 1) : P (16, r − 2) = 3 : 4, find r.
Concept: undefined >> undefined
If n +5Pn +1 =\[\frac{11 (n - 1)}{2}\]n +3Pn, find n.
Concept: undefined >> undefined
In how many ways can five children stand in a queue?
Concept: undefined >> undefined
From among the 36 teachers in a school, one principal and one vice-principal are to be appointed. In how many ways can this be done?
Concept: undefined >> undefined
Four letters E, K, S and V, one in each, were purchased from a plastic warehouse. How many ordered pairs of letters, to be used as initials, can be formed from them?
Concept: undefined >> undefined
Four books, one each in Chemistry, Physics, Biology and Mathematics, are to be arranged in a shelf. In how many ways can this be done?
Concept: undefined >> undefined
Find the number of different 4-letter words, with or without meanings, that can be formed from the letters of the word 'NUMBER'.
Concept: undefined >> undefined
