Question

A gaurd of $12$ men is formed from a group of`n` soliders. It is found that $2$ particular soliders A and B are $3$ times as often together on guard as $3$ particulars soliders C,D and E. Then n is equal to

• A. $28$
• B. $27$
• C. $32$
• D. $36$

Answer 1

Answer: (C)

$32$

Total number of men$=12$

Group of soldiers $=n$

First we found that $2$ particular soldier$=12-2=10$

Then, the value is ${}^{n-2}{C}_{10}$ ……… (1)

Now we found that 3 times as 3 particulars soldiers $=12-3=9$

Then, the value is $3{\times }^{n-3}{C}_9$ ……… (2)

According to given question

By equation (1) and (2) to and we get,

${}^{n-2}{C}_{10}=3{\times }^{n-3}{C}_9$

$\Rightarrow \frac{(n-2)!}{10!(n-2-10)!}=3\times \frac{(n-3)!}{9!(n-3-9)!}$

$\Rightarrow \frac{(n-2)(n-3)!}{10\times 9!(n-12)!}=3\times \frac{(n-3)!}{9!(n-12)!}$

$\Rightarrow \frac{(n-2)}{10}=3$

$\Rightarrow n-2=30$

$\Rightarrow n=32$

Hence, it is complete solution .

Option $C$ is correct.