Question

In an election three districts are to be canvassed by $2,3$ and $5$ men respectively. If $10$ men volunteer, the number of ways they can be alloted to the different district is:

• A. $\frac{10!}{2!3!5!}$
• B. $\frac{10!}{2!5!}$
• C. $\frac{10!}{(2!{)}^{2}5!}$
• D. $\frac{10!}{(2!{)}^{2}3!5!}$

Answer 1

Answer: (A)

$\frac{10!}{2!3!5!}$

No of men $=10$

Three districts are to be canvassed by 2, 3 and 5 men.

No. of ways to do so=no. of ways of reflecting 5 voluntary for 1 district $\times$ No. of ways of reflecting 3 voluntary court of remaining 5 for 2nd district $\times$ No. of ways of reflecting 2 voluntaries from remaining 2 for 3rd district

$={}^{10}{C}_5\times {}^5{C}_3\times {}^2{C}_2$

$=\frac{10!}{5!\times 5!}\times \frac{5!}{3!\times 2!}\times 1$

$=\frac{10!}{5!\times 3!\times 2!}$

So, option A is correct.