# 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

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

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
$\dfrac{n!}{n^{n}}=\dfrac{3}{32}=\dfrac{4!}{4^{4}}$