Let A and B be two finite sets having m and n | vedclass

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(B) The total number of functions (mappings) from a set $A$ with $m$ elements to a set $B$ with $n$ elements is given by $n^m$.An injection (one-to-on

Vedclass · Accepted Answer

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

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(B) The total number of functions (mappings) from a set $A$ with $m$ elements to a set $B$ with $n$ elements is given by $n^m$.An injection (one-to-one function) exists only if $m \le n$. The number of ways to choose $m$ distinct elements from $B$ and arrange them is given by the permutation formula $P(n, m) = \frac{n!}{(n - m)!}$.Therefore,the number of injective mappings is $\frac{n!}{(n - m)!}$.The probability $P$ of selecting an injection is the ratio of the number of injective mappings to the total number of mappings:$P = \frac{	ext{Number of injective mappings}}{	ext{Total number of mappings}} = \frac{\frac{n!}{(n - m)!}}{n^m} = \frac{n!}{(n - m)! n^m}$.

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

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