Out of 5 apples, 10 mangoes and 15 oranges, any 15 fruits are to be distributed among two persons. Then the total number of ways of distribution?

1) 66

2) 36

3) 60

4) None of these

Answer: (1) 66

Solution: Give, there 5 apples, 10 mangoes and 15 oranges

Total fruits = 5 + 10 + 15 = 30

Any 15 fruits are to be distributed among two persons

Therefore, number of ways of distribution = Coefficient of x¹⁵ in (1+x+x²+…+x⁵) (1+x+x²+..+x¹⁰)(1+x+x²+..+x¹⁵)

= 66