# Thread: 4C3 or 12C8?

1. ## 4C3 or 12C8?

A group of 12 persons are available for use in a study. Four are to be selected to receive an experimental treatment, while the remaining persons will serve as the control group. In how many ways can the control group be composed?

2. ## Re: 4C3 or 12C8?

Originally Posted by nycmath
A group of 12 persons are available for use in a study. Four are to be selected to receive an experimental treatment, while the remaining persons will serve as the control group. In how many ways can the control group be composed?
Is it true that $\dbinom{12}{4}=\dbinom{12}{8}~?$

Does it matter if you choose the control group or the experimental group?

3. ## Re: 4C3 or 12C8?

I subtracted the 4 people selected for the experimental group from 12. This left 8 to be selected for the control group.
I then said it must be 12C8.