Question

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

• A. $6!-6$
• B. $6^6-6$
• C. $6^6-6!$
• D. $6!$

Answer 1

The correct option is C $6^6-6!$

Total number of functions from $A$ to $A=6^6$
Number of bijections from $A$ to $A=6!$
$\therefore$ Total number of functions which are not bijections$=$Total number of functions from $A$ to $A$$-$Number of bijections from $A$ to $A$ $=6^6-6!$