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A fruit basket contains 4 oranges, 5 apples and 6 mangoes. The number of ways a person makes a selection of fruits from among the fruits in the basket is?
$
  {\text{A}}{\text{. }}209 \\
  {\text{B}}{\text{. }}210 \\
  {\text{C}}{\text{. }}211 \\
  {\text{D}}{\text{. }}212 \\
 $

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Last updated date: 13th Jun 2024
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Answer
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Hint: Here we go through by the property of permutation and combination. And always keep in mind that whenever it is not explicitly mentioned that fruits are distinct, we take them as identical.

Complete step-by-step answer:
Here in the question it is given that there are 4 identical oranges, 5 identical apples and 6 identical mangoes
We can say it as,
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 (6+1) =7 ways
Therefore total number of ways in which all of three types of fruits can be selected (the number of any type of fruits may also be 0) =$5 \times 6 \times 7 = 210$
But in these 20 selections, there is one selection where all fruits are 0, hence we reduce selection.
$\therefore $The required number of selection is 210-1=209.

So, the correct answer is “Option A”.

Note: Whenever we face such a question the key concept for solving the question is first of all find the total number of ways of selecting each fruit one by one and then multiply it to get the total number of selection and always keep in mind to subtract the common things which are counted in it. Here in this question we counted the selection of zero fruits one time so at the end we subtract it to get the answer.