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

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14.Probability

easy

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

A

$\frac{2}{{19}}$

B

$\frac{3}{{29}}$

C

$\frac{{17}}{{19}}$

D

$\frac{4}{{19}}$

Solution

(c) The total number of ways in which $3$ integers can be chosen from first $20$ integers is $^{20}{C_3}.$

The product of three integers will be even if at least one of them is even.

$\therefore $ Required probability $ = 1 -$ Probability that none is even

$ = 1 – \frac{{^{10}{C_3}}}{{^{20}{C_3}}} = 1 – \frac{2}{{19}} = \frac{{17}}{{19}}.$

Standard 11

Mathematics

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(JEE MAIN-2023)