Question

Four distinct numbers are selected from first 100 natural numbers such that each number is divisible by both 3 and 5. The number of selections possible is
___

Answer 1

Soln:

A number divisible by 3 as well as 5 has to divisible by 15. In the first 100 natural numbers, there are 6 such numbers-> 15, 30, 45, 60, 75, 90

Favorable number of ways = ${}^6{C}_4$.

Answer is 15.