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
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B
330
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C
209
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D
None of these
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Solution

## The correct option is C 209In the selection of fruits, fruits of same type are treated as identical. Number of selections of any number of oranges from 4 oranges=4+1Number of selections of any number of apples from 5 apples=5+1Number of selections of any number of mangoes from 6 mangoes=6+1Thus the total number of selections of any fruit from the basket=(4+1)(5+1)(6+1)=210But in one of these selections, there in one which contains no fruit . so excluding this, the number of required selection=209

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