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Question: Three integers are chosen at random from the first 20 integers. The probability that their product i...

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

A

219\frac { 2 } { 19 }

B

329\frac { 3 } { 29 }

C

1719\frac { 17 } { 19 }

D

419\frac { 4 } { 19 }

Answer

1719\frac { 17 } { 19 }

Explanation

Solution

The total number of ways in which 3 integers can be chosen from first 20 integers is 20C3{ } ^ { 20 } C _ { 3 } The product of three integers will be even if at least one of them is even.

∴\thereforeRequired probability = 1 – Probability that none is even

=1−10C320C3=1−219=1719= 1 - \frac { { } ^ { 10 } C _ { 3 } } { { } ^ { 20 } C _ { 3 } } = 1 - \frac { 2 } { 19 } = \frac { 17 } { 19 }