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

• A. 210
• B. 330
• C. 209
• D. None of these

Answer 1

Answer: (C)

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 $=6+1$.
$\therefore$ Number of selections of any number of fruits from the basket $=(4+1)(5+1)(6+1)$
$=5\times 6\times 7=210$.
But in one of these selections, there is one which contains no fruits.
Excluding this selection, the required number of selections $=210-1=209$.