Three integers are chosen at random from the first `20` integers. The probability that their product is even is

Options

A. a) `2/(19)`
B. b) `3/(29)`
C. c) `(17)/(19)`
D. d) `4/(19)`

Answer

c) `(17)/(19)`

Explanation

Total sample space `= 20_(C_3)`


In first `20` integers, `10` integers are odd and other `10` should be even.


Product of `3` integers will be even, if at least one of the integers is even.


`Even*Odd*Odd=Even`


`Even*Odd*Even=Even`


`Even*Even*Even=Even`


Required probability = 1- Probability of no integers is even.


`= 1- (10_(C_3))/(20_(C_3))`


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