Permutations

Question

The number of permutations of ‘n’ different things taken not more than ‘r’ at a time, with
repetitions   being allowed, is
(a) (n^r – 1)/ (n – 1)     (b) (n^r – 1) / (n – 1)!
(c) n(n^r – 1)/ (n – 1)   (d) (n^r – 1) / n!

Answer 1

suppose we have n objects and we are allowed to take at any time r or less than r objects.

 

For r=1, that means selecting 1 object from n and permuting there are 'n' ways of doing it.

for r=2, We have n*n ways because repetition is allowed.

similarly for r=3, n*n*n different arrangements we can make.

So our solution is n+ n*n + n*n*n +............n^r

which is sum of 'r' terms in GP with common ratio=n.

which is  n(n^r -1) / (n-1).

Option C.

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