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Question

A fruit basket contains 4 oranges, 5 apples and 6 mangoes. The number of ways a person make selection of fruits from among the fruits in the basket is?

A
119
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B
209
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C
208
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D
210
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Solution

The correct option is A 209
Whenever it is not explicity mentioned that fruit and distint, We take them as identical. 0 or more orange can be selected from 4 identical oranges in (4+1)=5 ways. 0 or more apples can be selected from 5 identical apples in (5+1)=6 ways.
0 or more mangoes can be selected from 6 identical mangoes in 7 ways.
Total no. of ways in which all of three types of fruits can be selected (the no. of any type of fruits may also be 0),
5×6×7=210,
But in these 20 selection, there is one selection where all fruits are 0, hence we reduce 1 selection.
the required no. =2101=209

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