A mapping is selected at random from mappings f: A→A, where set A={1,2,3,4...............n} If the probability that mapping is injective is 332, then the value of n is

Total no of mapping = nnNo of one – one mapping = n! p=n!nn =(n−1)!n(n−1) =332=664=3!43n=4

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A mapping is selected at random from mappings $f : A \to A$ , where set $A = {1, 2, 3, 4............... n}$ If the probability that mapping is injective is $\frac{3}{32},$ then the value of $n$ is

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answer is 4.

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Detailed Solution

Total no of mapping = $n^{n}$
No of one – one mapping = n! $p = \frac{n!}{n^{n}} = \frac{(n - 1)!}{n^{(n - 1)}} = \frac{3}{32} = \frac{6}{64} = \frac{3!}{4^{3}}$

n=4

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