Question

The total number of selections of atleast one fruit which can be made from 3 bananas, 4 apples and 2 oranges is

• A. $515$
• B. $511$
• C. $512$
• D. none of these

Answer 1

Answer: (B)

$511$

Number of selection of at least one fruit $=$ Number of selection of one fruit $+$ No. of selection of two fruit $+$ .......... $+$ No. of selection of $9$ fruit

$={}^9{C}_1+{}^9{C}_2+{}^9{C}_3+{}^9{C}_4+{}^9{C}_5+{}^9{C}_6+{}^9{C}_7+{}^9{C}_8+{}^9{C}_9$

$=9+36+84+126+126+84+36+9+1$

$=511$

Thus, there ar $511$ ways.

So, option (d) is correct.