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. $119$
• B. $209$
• C. $208$
• D. $210$

Answer 1

Answer: (B)

$209$

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.

$\therefore$ 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 $0$),

$5\times 6\times 7=210$,

But in these $20$ selection, there is one selection where all fruits are $0$, hence we reduce $1$ selection.

$\therefore$ the required no. $=210-1=209$