Let A and B be two finite sets having m and n elements respectively such that m le n., A mapping is

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14.Probability

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Let $A$ and $B$ be two finite sets having $m$ and $n$ elements respectively such that $m \le n.\,$ A mapping is selected at random from the set of all mappings from $A$ to $B$. The probability that the mapping selected is an injection is

A

$\frac{{n\,!}}{{(n - m)\,!\,{m^n}}}$

B

$\frac{{n\,!}}{{(n - m)\,!\,{n^m}}}$

C

$\frac{{m\,!}}{{(n - m)\,!\,{n^m}}}$

D

$\frac{{m\,!}}{{(n - m)\,!\,{m^n}}}$

Solution

(b) As we know the total number of mappings is ${n^m}$ and number of injective mappings is $\frac{{n\,\,!}}{{(n – m)\,!{n^m}}}$.

Standard 11

Mathematics

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