Some couples participated in a mixed doubles badminton tournament. If the number of matches played, so that no couple played in a match, is 840, then the total numbers of persons, who participated in the tournament, is ______.

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answer is 16.

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Detailed Solution

Number of couples = n
$\begin{array}{l} ^{n} C_{2} \times^{n - 2} C_{2} \times 2 = 840 \\ \Rightarrow n (n - 1) (n - 2) (n - 3) = 5 \cdot 6 \cdot 7 \cdot 8 \\ n = 8 \end{array}$
Total number of persons = 16

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