232 (Ans)
f : A → A Function from set A to A itself.
Total Functions possible from A → A are 44 {$\because$ Number of Functions
from A → B are |B||A| }
Now we have a property that if |A| = |B| , then
if function is one-one then it is onto and vice-versa.
Now Number of one-one & onto functions from A → A are 4!
$\because$ 1 has 4 choices
2 has 3 choices {we assigned a number to 1}
3 has 2 choices
4 has 1 choice left.
So, Total Number of Functions = 44 = 256
Number of functions which are one-one/ onto = 4! = 24
So, Number of functions possible on A which are neither
one-one nor onto is 256 - 24 = 232 (Ans)