A function is selected from all functions on set S = {1, 2, 3,.... n} to itself. If the probability that it is one-one is $\frac{3}{32}$ , then n is equal to ___.

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Solution

The total number of functions is $n^{n} .$
The number of one-one function is n!.
$∴$ Required probability $= \frac{n!}{n^{n}} = \frac{3}{32} = \frac{6}{64} = \frac{24}{256} = \frac{4!}{4^{4}}$
$∴ n = 4$

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A function is selected from all functions on set S = {1, 2, 3,.... n} to itself. If the probability that it is one-one is 332, then n is equal to ___.

The total number of functions is nn. The number of one-one function is n!. ∴ Required probability =n!nn=332=664=24256=4!44 ∴n=4

A function is selected from all functions on set S = {1, 2, 3,.... n} to itself. If the probability that it is one-one is $\frac{3}{32}$ , then n is equal to ___.

The total number of functions is $n^{n} .$
The number of one-one function is n!.
$∴$ Required probability $= \frac{n!}{n^{n}} = \frac{3}{32} = \frac{6}{64} = \frac{24}{256} = \frac{4!}{4^{4}}$
$∴ n = 4$