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

Options

A. `.^(5)C_(4)(4/5)^(4)1/5`
B. `(4/5)^(4)1/5`
C. `.^(5)C_(1)1/5(4/5)^(4)`
D. None of these

Explanation

To solve the problem, we need to find the probability that out of five students, four are swimmers, given that the probability that a student is not a swimmer is \( \frac{1}{5} \).

### Step-by-Step Solution:

1. **Identify the Probability of Being a Swimmer:**
- The probability that a student is not a swimmer is given as \( q = \frac{1}{5} \).
- Therefore, the probability that a student is a swimmer is:
\[
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