BPSC 48th to 52nd Exam Prelims 2008 Solved Paper

From the question The probability that the student is not a swimmer $=\frac{1}{5}$
The probability that the student is a swimmer $=1-\frac{1}{5}=\frac{4}{5}$
$\mathit{p}=\frac{4}{5},\mathit{d}=\frac{1}{5}$
$\mathit{p}=5,\mathit{r}=4$
Now, probability that out of 5,4 are swimmers
$=5_{{\mathit{C}}_4}{\left(\frac{4}{5}\right)}^4\left(\frac{1}{5}\right)$
$=5\times {\left(\frac{4}{5}\right)}^4\times \frac{1}{5}={\left(\frac{4}{5}\right)}^4$