Question

A guard of 15 men is formed form a group of n soldiers. The number of times two particular soldiers will be guards

• A. $\frac{n!}{13!2!}$
• B. $\frac{n-2}{13!}$
• C. $\frac{(n-2)!}{13!(n-15)!}$
• D. $\frac{(n-2)!}{13!12!}$

Answer 1

Answer: (C)

$\frac{(n-2)!}{13!(n-15)!}$

Given there are $n$ soldiers out of which 2 are guards. Thus there are $n-2$ remaining soldiers out of which we have to select $15-2=13$ soldiers for guards.
Hence number of ways of selection is ${=}^{n-1}{C}_{15-2}{=}^{n-2}{C}_{13}=\frac{(n-2)!}{13!(n-15)!}$