**Question **: One mapping is selected at random from all mappings of the set S={1,2,3,…,n} into itself. If the probability that the mapping is one-one is 3/32, then the value of n is

(A) 2

(B) 3

(C) 4

(D) none of these

**Answer **: option (C)

**Solution **:

The total number of mapping is n^{n}. The number of one-one mapping is nc_{1} n-1C_{1}…1c_{1}=n!, hence the probability is

\dfrac{n!}{n^{n}}=\dfrac{3}{32}=\dfrac{4!}{4^{4}}
Comparing we get, n=4.

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