Question

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

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

Answer 1

Answer: (A)

$5\times \underset{–}{|11}$

Finding no. of such functions is same as putting 11 balls in 10 boxes with each box getting at least one ball. Then the only possible way is to put 2 balls in a box which can be done in ${}^{11}{C}_2$ ways.

${}^{11}{C}_2{\times }^9{C}_1{\times }^8{C}_1..................{.}^1{C}_1$

$=\frac{11\times 10}{2}\times 9\times 8\times \mathrm{7.................................}$

$11!\times 5$