First slide

Combinations

Question

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

Moderate

A

210
B

330
C

209
D

None of these

Solution

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.

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