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Standard XII

Mathematics

Combination with Restrictions

A guard of 12...

Question

A guard of 12 men is formed from $n$ soldiers. If A and B are three times as often together on guard as C, D, E then $n =$

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Solution

The correct option is A 32
$A, B$ in 12 $=$ 3 $\times C, D, E$ in $12$
$\Rightarrow^{n - 2} C_{10} = {3.}^{n - 3} C_{9}$
$\Rightarrow \frac{(n - 2)!}{(n - 12)! 10!} = 3. \frac{(n - 3)!}{(n - 12)! 9!}$
$\Rightarrow n - 2 = 10 \times 30 \Rightarrow n = 32$

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Similar questions

Q. A guard of 12 men is formed from a group of n soldiers in all possible ways. Find :
(i)The number of times two particular soldiers A and B are together on guard.
(ii)The number of times' three particular soldiers C, D, F are together on guard.
(iii)Also find h if it is found that A and B are three times as often together on guard as C, D,E are.

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A guard of 12 men is formed from n soldiers. If A and B are three times as often together on guard as C, D, E then n=

The correct option is A 32A,B in 12 = 3 ×C,D,E in 12⇒n−2C10=3.n−3C9⇒(n−2)!(n−12)!10!=3.(n−3)!(n−12)!9!⇒n−2=10×30⇒n=32

A guard of 12 men is formed from $n$ soldiers. If A and B are three times as often together on guard as C, D, E then $n =$

The correct option is A 32
$A, B$ in 12 $=$ 3 $\times C, D, E$ in $12$
$\Rightarrow^{n - 2} C_{10} = {3.}^{n - 3} C_{9}$
$\Rightarrow \frac{(n - 2)!}{(n - 12)! 10!} = 3. \frac{(n - 3)!}{(n - 12)! 9!}$
$\Rightarrow n - 2 = 10 \times 30 \Rightarrow n = 32$