Question

There are 4 mangoes, 3 apples, 2 oranges and 1 each of 3 other varieties of fruits. The number of ways of selecting at least one fruit of each kind is

• A. 10!
• B. 9!
• C. 4!
• D. none of these

Answer 1

Answer: (C)

4!

To find the number of ways of selecting at least one fruit of each kind
No of way of selecting 1 mango from 4 mangoes is ${}^4{\text{C}}_1$
No of way of selecting 1 mango from 3 apples is ${}^3{\text{C}}_1$
No of way of selecting 1 mango from 2 oranges is ${}^2{\text{C}}_1$
there is only one way selecting one fruit from one
$\therefore$ total no of ways of selection =4$\times$3$\times$2$\times$1$\times$1$\times$1=4!