Question

The number of onto functions from the set $\{1,2,....11\}$ to the set $\{1,2,....10\}$ is

• A. $5\times 11!$
• B. $10!$
• C. $\frac{11!}{2}$
• D. $10\times 11!$

Answer 1

The correct option is D $10\times 11!$

Let $A=\{1,2,.....11\}$
$\therefore$ $n\left(A\right)=11$ and $B=\{1,2,......10\}$
$\therefore$ $n\left(B\right)=10$
$\therefore$ Hence number of onto function
$={{}^{n\left(A\right)}C}_{n\left(B\right)}\times n\left(B\right)!\times n\left(B\right)$
$={{}^{11}C}_{10}\times 10!\times 10$
$=(11\times 10!)\times 10=11!\times 10$