A is a set having 6 distinct elements. The number of distinct fun… - Vidyadip

MCQ

A is a set having 6 distinct elements. The number of distinct functions from A to A which are not bijection is

A
$6!-6$
B
$6^6-6$
✓
$6^6-6!$
D
$6!$

✓

Answer

Correct option: C.

$6^6-6!$

(C)
The number of functions from a finite set A into a finite set $B =[ n ( B )]^{ n ( A )}$
The number of bijections from a finite set A onto a finite set B is
$n ( A )!; \quad$ if $n ( A )= n ( B )$
0 ; $\quad$otherwise
total number of distinct functions from
$A \rightarrow A = n ^{ n }=6^6$, and
number of bijections $=n!=6!$
∴ Number of functions which are not bijections
$=6^6-6!$

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