JEE Main 2026 (Online) 22nd January Morning ShiftQuestion 1
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 :
Probability
Solution
Multiples of 3 up to 50: 16; others: 34. $P(\text{not divisible})=\frac{\binom{34}2}{\binom{50}2}=\frac{561}{1225}$, so $P=1-\frac{561}{1225}=\frac{664}{1225}$.