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

JEE Main · 2026 · 22 Jan 2026 · Shift 1 · Probability

Two distinct numbers a and b are selected at random from

1, 2, 3, \dots, 50

. The probability, that their product ab is divisible by 3, is

(A) $\frac{561}{1225}$
(B) $\frac{664}{1225}$ ✓ Correct
(C) $\frac{272}{1225}$
(D) $\frac{8}{25}$

Answer: (B)

Solution

Between

1

and

50

there are

16

multiples of

3

and

34

non-multiples. The product

ab

is divisible by

3

unless both chosen numbers avoid

3

, so

P = 1 - \frac{( 2 34 )}{( 2 50 )} = 1 - \frac{561}{1225} = \frac{664}{1225} .

JEE Main · 2026 · 22 Jan 2026 · Shift 1 · Single correct option

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