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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

User Genba
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1 Answer

4 votes

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.

User Sombir Kumar
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8.6k points
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