Here we have a combination without repetition (the order doesn't matter but you can repeat an athlete). The formula is:
[tex]C(n,r)=\frac{n!}{r!(n-r)!}[/tex]Where n is the total number of athletes, and r is the number of athletes you have to select, then n=7 and r=4, then:
[tex]\begin{gathered} C(7,4)=\frac{7!}{4!(7-4)!} \\ C(7,4)=\frac{7!}{4!(3)!} \\ C(7,4)=\frac{5040}{24\times6} \\ C(7,4)=\frac{5040}{144} \\ C(7,4)=35 \end{gathered}[/tex]Thus, 35 four-person relay teams can be selected among the seven athletes.
