Ok so what we have is: out of 14 female nurses and 6 male nurses, we must have a shift of 6 people on the night shift. What we have to know is the basic counting principle, which states that having m possibilities for one experiment and n possibilities for another experiment means that you have a total of m*n possible outcomes. So to have 2 male nurses, we have to choose from 4 male nurses, which is one experiment, so that will come out to be 4*3/2*1, which is 6 different outcomes, and for the other experiment, we will choose 4 female nurses out of 14 female nurses, which will give us 14!/(4!10!). So the number of possibilities is 1001. So then the total number of combinations is 1001*6, which is 6006 different ways it can be formed if we have exactly 2 male nurses. Here you are.
