Question
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
JEE Main
Mathematics
Probability
2026
JEE Main 2026 (22 January Shift 1)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 272 1225
- B. 561 1225
- C. 664 1225
- D. 8 25
Answer
C. 664 1225
Step-by-step solution
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 .
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