(D) Let $n$ be the number of couples. The total number of persons is $2n$.To form a match,we select $2$ couples out of $n$ in ${}^nC_2$ ways.From each

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(D) Let $n$ be the number of couples. The total number of persons is $2n$.To form a match,we select $2$ couples out of $n$ in ${}^nC_2$ ways.From each of the $2$ selected couples,we select $1$ person of opposite gender in $2 \times 2 = 4$ ways.Thus,the number of matches is ${}^nC_2 \times 4 = 840$.${}^nC_2 = \frac{840}{4} = 210$.$\frac{n(n-1)}{2} = 210 \Rightarrow n(n-1) = 420$.Since $21 \times 20 = 420$,we have $n = 21$.Total persons $= 2n = 2 \times 21 = 42$.

Class 11 Mathematics Permutation and Combination Geometrical problems

Medium

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

JEE MAIN 2023 All JEE MAIN

A
$14$
B
$12$
C
$10$
D
$16$

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

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