Distributing 12 distinct balls to 5 different persons. Actually , my doubt is about number of ways of distributing 12 distinct balls to 5 different persons such that 3 persons get 2 balls each and 2 persons get 3 balls each.
There is another question in this site about "How many ways to divide group of 12 people into 2 groups of 3 people and 3 groups of 2 people?"
But my question is slightly different.
Solutions with explanation is needed. Thank you anyways for your help!

I believe that the correct answer is the product of:


*

*The number of ways to choose the persons: $\frac{5!}{3!2!}=10$

*The number of ways to choose the balls: $\frac{12!}{2!2!2!3!3!}=1663200$

