Three integers are chosen at random from the set of first 20 natural numbers. The chance that their product is a multiple of 3 is

The total number of ways of selecting 3 integers from 20 natural numbers is 20C3 = 1140. Their product is a multiple of 3 means at least one number is divisible by 3. The numbers which are divisible by 3 are 3, 6, 9, 12, 15, l8 and the number of ways of selectin g at least one of them is  6C1×14C2+6C2×14C1+6C3=776. Hence, the required probability is 776/1140 = 194/285.