The probability that a student is not a swimmer is $\frac{1}{5}$. Then the probability that out of live students, four are swimmers is :

${^5C}_4\left(\frac{4}{5}\right)^4\frac{1}{5}$

The correct answer is option (1) → ${^5C}_4\left(\frac{4}{5}\right)^4\frac{1}{5}$

$P(S)=\frac{4}{5},P(\overline{S})=\frac{1}{5}$

then probability of 4 out of 5 to be swimmers

$⇒{^5C}_4\left(\frac{4}{5}\right)^4\frac{1}{5}$