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

${ }^5 C_4\left(\frac{1}{5}\right)\left(\frac{4}{5}\right)^4$

A = No. of students who are bowler out of 5 = 4

Probability that a student is not a bowler is (q) = \(\frac{1}{5}\)

Probability that a student is a bowler is (p) =  1 - Probability that a student is not a bowler

Probability that a student is a bowler is (p) =  1 - \(\frac{1}{5}\) = \(\frac{4}{5}\) 

Binomial distribution of A  P(A = a) = nCa q^n-a p^a

 P(A = )  = 5C4 q1 p⁴

= ${ }^5 C_4\left(\frac{1}{5}\right)\left(\frac{4}{5}\right)^4$

The correct answer is Option (4) → ${ }^5 C_4\left(\frac{1}{5}\right)\left(\frac{4}{5}\right)^4$