Two distinct numbers a and b are selected at random from 1,2,3, , 50 . The probability, that their product a b is divisible by 3, is

Correct answer: C. (664)/(1225) Total ways = 50 2 = 1225 . ab is divisible by 3 iff at least one of a, b is divisible by 3. Multiples of 3 in \ 1, ,50\ : 3,6, ,48 16 numbers. Non-multiples of 3: 34 . P(neither divisible by 3) = 34 2 50 2 = (561)/(1225) . P(ab divisible by 3) = 1 - (561)/(1225) = (664)/(1225) .

JEE Main 202622 JanuaryMorning Shift

Exam: JEE Main
Year: 2026
Date: 22 January
Shift: Morning Shift
Subject: Mathematics
Chapter: Probability

JEE Main 2026 · 22 January · Morning Shift · Mathematics · Probability

Two distinct numbers a and b are selected at random from 1,2,3, ,...

Two distinct numbers

a

and

b

are selected at random from

1,2,3, \ldots, 50

. The probability, that their product

a b

is divisible by 3, is

Options

A $\frac{272}{1225}$
B $\frac{561}{1225}$
C $\frac{664}{1225}$
D $\frac{8}{25}$

Correct answer

C. $\frac{664}{1225}$

Step-by-step solution

Total ways

= \binom{50}{2} = 1225

ab

is divisible by 3 iff at least one of

a, b

is divisible by 3.
Multiples of 3 in

\{1,\ldots,50\}

3,6,\ldots,48 \Rightarrow 16

numbers. Non-multiples of 3:

34

P(\text{neither divisible by 3}) = \frac{\binom{34}{2}}{\binom{50}{2}} = \frac{561}{1225}

P(ab \text{ divisible by 3}) = 1 - \frac{561}{1225} = \frac{664}{1225}

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