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?

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?