A ward in a city hospital has 15 nurses due to work on Frida

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?

Solution

To arrange for nurses in the first shift, there are 15 nurses available, out of which 5 has to be chosen.

This can be done in ^15C_5 ways.

In the next shift, there are 10 nurses available. Five nurses out of them can be put on duty in [^10C_5] ways.

Out of the remaining 5 nurses all five has to be put on duty. This can be done in [^5C_5] ways.

Since this is a sequential selection, the overall number of possibilities can be ontained by multiplication.

Thus, the number of ways 15 nurses can be arranged for duty in the three shifts = [^15C_5 *^10C_5 *^5C_5]

=756756

=>answer