Question

In how many ways $10$ different objects can be distributed between $3$ children of different ages so that each child receives at least $2$ objects and the number of receiving of each child is inversely proportional to his age?

• A. $2520$
• B. $15120$
• C. $5040$
• D. $10080$

Answer 1

The correct option is A $2520$

The only possibility is that receiving of children must be $5,3$ and $2$ inversely proportional to their ages.
Number of ways $=\frac{10!}{2!3!5!}=2520$