The probability that a student is not a swimmer is $1 fifth.$ Then the probability that out of five students, four are swimmers is
$straight C presuperscript 5 subscript 4 space open parentheses 4 over 5 close parentheses to the power of 4 space 1 fifth$
$open parentheses 4 over 5 close parentheses to the power of 4 space 1 fifth$
$straight C presuperscript 5 subscript 1 space open parentheses 4 over 5 close parentheses to the power of 4$

None of these

Solution

straight C presuperscript 5 subscript 4 space open parentheses 4 over 5 close parentheses to the power of 4 space 1 fifth

Here n = 5
$straight q space equals space 1 fifth comma space space space space straight p space equals space 1 space minus space straight q space equals space 1 minus 1 fifth space equals space 4 over 5$
$therefore space space space space straight P left parenthesis 4 space are space swimmer right parenthesis space equals space straight P left parenthesis 4 right parenthesis space equals space straight C presuperscript 5 subscript 4 space open parentheses 1 fifth close parentheses to the power of 1 space open parentheses 4 over 5 close parentheses to the power of 4 space equals space straight C presuperscript 5 subscript 4 space open parentheses 4 over 5 close parentheses to the power of 4 space open parentheses 1 fifth close parentheses$
∴ (A) is correct answer.

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