There are four oranges, five apples and six mangoes in a fruit basket. The number of ways in which a person can make a selection of fruits among the fruits in the basket, is

In selection of fruits, fruits of the same type are treated as identical.

Number of selections of any number of oranges from 4 oranges = 4 + 1.

Number of selections of any number of apples from 5 apples = 5 + 1.

Number of selections of any number of mangoes from 6 mangoes = 6 + 1.

∴ Number of selections of any number of fruits from the basket = (4 + 1) (5 + 1) (6 + 1) = 5 × 6 × 7 = 210.

But in one of these selections, there is one which contains no fruits. Excluding this selection, the required number of selections = 210 – 1 = 209.