The Total Number Of Injective Mappings From A Set With M Elements Of Distinct Functions From A to A is

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Question

The total number of injective mappings from a set with m elements of distinct functions from A to A is

mⁿ
n^m
n!

easy

Solution

Correct option is

can have n images in B, but the elements a₂will have only (n – 1) images as the mappings are to be one-one (injective).

Similarly the elements a₃will have (n – 2) images. Hence the total number of mappings will be

= n(n – 1) (n – 2)…

= n (n – 1) (n – 2) …(n – m – 1)

Multiply above and below by

(n – m) (n – m – 1)…3. 2. 1

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