Two distinct numbers and are selected at random from . The probability that their product is divisible by 3, is [2026]

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Solution

Q.
Two distinct numbers $a$ and $b$ are selected at random from $1, 2, 3, \dots, 50$ . The probability that their product $a b$ is divisible by 3, is [2026]

1 $\frac{664}{1225}$

2 $\frac{561}{1225}$

3 $\frac{8}{25}$

4 $\frac{272}{1225}$

Ans.
(1)

$Required probability = 1 - (product not divisible by 3)$

$Multiple of 3 = 16$

$Not multiple of 3 = 34$

$= 1 - \frac{{}^{34}C_{2}}{{}^{50}C_{2}}$

$= \frac{664}{1225}$

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