We want to choose 4 people and we have 6 people to choose from. This is a combination of 6, 4 by 4. Also called six choose four.
The following formula:
[tex]_rC_n=\frac{n!}{r!(n-r)!}[/tex]
Is the combination of [tex]r[/tex] objects choosen from a total of [tex]n[/tex]. It's [tex]n[/tex] choose [tex]r[/tex].
For our problem, we just need to compute the following:
[tex]_4C_6=\frac{6!}{4!(6-4)!}=\frac{6\times5\times4!}{4!2!} =\frac{6\times5}{2\times1} =15[/tex]
Thus
[tex]\boxed{_4C_6=15}[/tex]
Therefore the answer is 15 different combinations
