Question

4 apples, 3 pineapples and 5 oranges has to be placed in 12 baskets and only one fruit can be placed in one basket. In how many ways it can be done?

• A. $12!$
• B. $4!\times 3!\times 5!$
• C. $\frac{12!}{(4!\times 3!\times 5!)}$
• D. $\frac{(4!\times 3!\times 5!)}{12!}$

Answer 1

The correct option is C $\frac{12!}{(4!\times 3!\times 5!)}$

12 fruits can be arranged in 12! Ways in 12 baskets.
But, 4 apples, 3 pineapples and 5 oranges are similar things.
Therefore, total number of ways possible $=\frac{12!}{(4!\times 3!\times 5!)}$