Question

In designing an experiment involving a treatment applied to 4 test subjects, researchers plan to use a simple random sample of 4 subjects selected from a pool of 48 available subjects. how many different simple random samples are possible?

Answer 1

There are 48 available subjects. Researchers should select 4 of them for their experiment. 
We should find the number of possible different random samples. The order of the selected subjects is not important. This means that we need to find how many different combinations of  subjects from total 48 are possible. A formula for the number of possible combinations of r objects from a set of n objects is: n!/r!(n-r)!. In our case n=48 and r=4:
C=48!/44!*4!=48*47*46*45*44!/44!*4!=48*47*46*45/4*3*2*1=4669920/24=
194580.