First slide

Permutations

Question

The total number of injective mappings from a set with m elements to a set with n elements for $m > n,$ is

Moderate

A

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

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

$n^{m}$
D

zero

Solution

If $A$ and B are two finite sets, and $f : A \to B$ is an injective mapping, then $n (A) \leq n (B)$
As $m > n$ , there does not exist any mapping from set with n elements.

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