The probability that a student is not a swimmer is `1/5` . Then the probability that out of five students, four are swimmers is (A) `^5C_4""(4/5)^4""1/5` (B) `(4/5)^4""1/5` (C) `^5C_1 1/5(4/5)^4` (D) None of these

Answer

`((4)/(5))^(4)`

Explanation

Let p be the probability that a student selected at rondom is a swimmer, which is given by `1-1//5=4//5.` The number of students selected is 5. Probability that exactly 4 students are swimmers is
`""^(5)C_(4)p^(4)q=5((4)/(5))^(4)((1)/(5))=((4)/(5))^(4)`