Question

Let $A=\{1,3,5,7\},$ $B=\{2,4,6,8\}$ and $f:A\to B.$ Then number of functions $f$ such that $f\left(i\right)\ne i+1,\forall i=1,3,5,7$ is

• A. $64$
• B. $24$
• C. $256$
• D. $81$

Answer 1

The correct option is D $81$

$f\left(i\right)\ne i+1$
$\Rightarrow f\left(1\right)\ne 2,f\left(3\right)\ne 4,f\left(5\right)\ne 6,f\left(7\right)\ne 8$
So, each of the elements in $A=\{1,3,5,7\}$ has $3$ choices in $B=\{2,4,6,8\}$
$\therefore$ Required number of functions
$=3\times 3\times 3\times 3=3^4=81$