(Q). In how many ways two numbers can be selected from 100, 101, 102, ……… 199 such that when these selected numbers are multiplied then the product is divisible by 3?
Solution:-
Numbers divisible by 3 are:-
& remaining 100 – 33 = 67 numbers are not multiple of 3.
Since product of two numbers is divisible by 3, it is possible only when at least one of them is multiple of 3.
∴ required number of ways
= if both the numbers are multiple of 3 + if only one number is multiple of 3
= ³³C₂ + ³³C₁×⁶⁷C₁ Answer