Question

Seven Olympic sprinters are eligible to compete in the 4 x 100 m relay race for the USA Olympic team. How many four-person relay teams can be selected from among the seven athletes

Answer 1

Here we have a combination without repetition (the order doesn't matter but you can repeat an athlete). The formula is:

`C(n,r)=(n!)/(r!(n-r)!)`

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:

`\begin{gathered} C(7,4)=(7!)/(4!(7-4)!) \\ C(7,4)=(7!)/(4!(3)!) \\ C(7,4)=(5040)/(24*6) \\ C(7,4)=(5040)/(144) \\ C(7,4)=35 \end{gathered}`

Thus, 35 four-person relay teams can be selected among the seven athletes.