Question

Shekar is one member of a group of $5$ persons. If $3$ out of these $5$ persons is to be chosen for a committee, find the probability of Shekar being in the committee

Answer 1

Total number of person are $5$.

The number of ways of choosing three persons is:

${}^5{C}_3=\frac{5!}{(5-3)!\times 3!}=\frac{5!}{2!\times 3!}=\frac{5\times 4\times 3\times 2\times 1}{2\times 1\times 3\times 2\times 1}=10$

Therefore, $n\left(S\right)=10$

Let $A$ denote the event of choosing $3$ persons including Shekar, therefore,

$n\left(A\right){=}^4{C}_2=\frac{4!}{(4-2)!\times 2!}=\frac{4!}{2!\times 2!}=\frac{4\times 3\times 2\times 1}{2\times 1\times 2\times 1}=6$

Thus, probability of choosing $3$ persons including Shekar is:

$P\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)}=\frac{6}{10}=\frac{3}{5}$

Hence, probability of Shekar being in committee is $\frac{3}{5}$.