Question

If $4$ of $12$ scooterists do not carry driving license, what is the probability a traffic inspector who randomly selects $4$ scooterists will catch $1$ for not carrying driving license.

Answer 1

The no.of ways of selecting 4 out of them are ${}^{12}{C}_4=495$

no .of ways of selecting 1 for not having a license is ${}^4{C}_1{\times }^8{C}_3$

$4\times 56=240$

Probability is $\frac{240}{495}=\frac{16}{33}$