# Math Help - Permutation

1. ## Permutation

Hi, I need help with this permutation problem. Can anyone please explain how to solve this problem in steps? Thanks in advance.

Q: In how many different ways can 5 pennies, 4 nickels, and 6 dimes be given to 15 children so that each child receives exactly 1 coin?

2. Originally Posted by Unknown
Q: In how many different ways can 5 pennies, 4 nickels, and 6 dimes be given to 15 children so that each child receives exactly 1 coin?
Note that we have only 15 coins.
Think of the children’s listed on a roster such as a roll book.
How many ways can we list 5 P’s, 4 N’s and 6 D’s next to those names?
Here is a hint: We can arrange the string “000111122222” in $\frac{{12!}}{{\left( {3!} \right)\left( {4!} \right)\left( {5!} \right)}}$.

3. I'm not sure if I'm doing this right, but would the setup for the problem be 15!/6!5!4! ...?

Because in total there are 15 to choose from and there are 3 different types of coins with a different value for each.

So would the answer be 630,630?

4. Originally Posted by Unknown
I'm not sure if I'm doing this right, but would the setup for the problem be 15!/6!5!4! ...?
So would the answer be 630,630?
Correct.