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sattari [20]
2 years ago
7

A tennis tournament has 2n contestants. We want to pair them up for the first round of singles matches. Show that the number of

different ways in which first round matches can be conducted is
Mathematics
1 answer:
ddd [48]2 years ago
4 0

There are

\dbinom{2n}2 = \dfrac{(2n)!}{2! (2n-2)!}

ways of pairing up any 2 members from the pool of 2n contestants. Note that

(2n)! = 1\times2\times3\times4\times\cdots\times(2n-2)\times(2n-1)\times(2n) = (2n-2)! \times(2n-1) \times(2n)

so that

\dbinom{2n}2 = \dfrac{(2n)\times(2n-1)\times(2n-2)!}{2! (2n-2)!} = \boxed{n(2n-1)}

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