Question

Let $A=\{1,2,3,4,5\}$ and $f:A\to A$ be an into function such that $f\left(i\right)\ne i,\forall i\in A,$ then number of such functions $f$ are

• A. $1024$
• B. $904$
• C. $980$
• D. None of these

Answer 1

Answer: (A)

$1024$

Since $f$ is a into function so one element in image have more than one pre omage in set $A$, so, for $f\left(i\right)\ne i\forall i\in A$,

Total number of such functions $=4\times 4\times 4\times 4\times 4=1024$