DemaniZ205009 DemaniZ205009

25-10-2022
Mathematics

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A half-marathon has 53 runners. A first-, second-, and third-place trophy will be awarded. Howmany different ways can the trophies be awarded?

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PratikE609210 PratikE609210

25-10-2022

Let's use the combination formula:

[tex]\begin{gathered} C(n,k)=nCk=\frac{n!}{k!(n-k)!} \\ n=53 \\ k=3 \\ C(53,3)=53C3=\frac{53!}{3!(50)!}=23426 \end{gathered}[/tex]

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