# Math Help - Permutation and Combination

1. ## Permutation and Combination

I am having trouble dealing with this question:
A ward in a city hospital has 15 nurses due to work on Friday. There are 3 shifts that need to be staffed by 5 nurses on each shift. How many different arrangements for staffing these 3 shifts are possible, assuming that each nurse only works 1 shift?

The answer is 756756 arrangements.
But i don't understand why this is the answer though.

2. ## Re: Permutation and Combination

Originally Posted by richardyuen2144
A ward in a city hospital has 15 nurses due to work on Friday. There are 3 shifts that need to be staffed by 5 nurses on each shift. How many different arrangements for staffing these 3 shifts are possible, assuming that each nurse only works 1 shift?
The answer is 756756 arrangements.
Think of the shifts as $A,~B,~\&~C$.
On the roster of nurses, we put five A's, five B's and five C', one letter by each name.
How many ways are there to arrange the string $AAAAABBBBBCCCCC~?$

3. ## Re: Permutation and Combination

Thank You Very Much

4. ## Re: Permutation and Combination

I don't really get why do u have to put the nurses that are in the same shift under the same letter? Why is the concept behind it? Would please explain to me?

5. ## Re: Permutation and Combination

Originally Posted by richardyuen2144
I don't really get why do u have to put the nurses that are in the same shift under the same letter? Why is the concept behind it? Would please explain to me?
It tell us what shift the nurse is assigned.
Any nurse with a B next her/his name is on the second shift.