Question

A fruit basket contains $4$ oranges, $5$ apples, $6$ mangoes. The number of ways person make selection of fruit from among the fruits in the basket is
(A) $210$
(B) $209$
(C) $208$
(D) None of these

Answer 1

First we observe how many fruits are in the basket.
Now we selected one by one of the fruits contained in the basket and also considered either no fruits.
Finally we find the number of ways people can select the fruits.

Complete step-by-step answer:
It is given that a fruit basket contains $4$ oranges, $5$apples, $6$mangoes.
The no. of ways a person makes selection of fruit from among the fruits in the basket.
In this kind of selection of fruits,
In Orange case, no. of oranges $= 4$
There is either no orange or one orange or two orange or three orange or four orange.
∴ Number of ways of orange selected $= 1 + 4{\text{ }} = 5$ ways
In apple case, no. of apples$= 5$
There is either no apple or one apple or two apple or three apple or four apple or five apple.
∴ Number of ways of apple selected$= 1 + 5 = 6$ways
In Mango case, no. of mango$= 6$
There is either no mango or one mango or two mango or three mango or five mango or six mango.
∴ Number of ways of mango selected $= 1 + 6 = 7$ ways
When we done no selection of a fruit than we need to subtract 1 from the entire selection of fruits
∴Total number of selecting fruits $= 5 \times 6 \times 7 - 1 = 209$ ways
Hence the correct answer is $209$

So, the correct answer is “Option B”.

Note: Finding the selected fruits from among the fruits. For that, subtract the number of fruits in the basket from the total number of selected fruits.