Number of ways of forming a committee of 6 members out of 5 Indians, 5 Americans and 5 Australians such that there will be at least one member from each country in the committee is

Step-by-step solution

The number of ways a could form in which at least one member from each country in the committee. We have triplets 1 , 1 , 4 → 3 1 , 2 , 3 → 3 ! = 6 2 , 2 , 2 → 1 Now total ways = 3 C 1 5 × C 1 5 × C 4 5 + 6 C 1 5 × C 2 5 × C 3 5 + C 2 5 × C 2 5 × C 2 5 = 375 + 3000 + 1000 = 4375