(16)

Given,

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,

Now Let total number of persons be 2n, so number of couples will be n

Now number of matches played, so that no couple played in a match is given by,

n C 2 . n-2 C 2 .2 = 840

{as if we choose couple as {A, B} and other couple as {C, D} and taking other two couple as {x, y} & {w, z}, so the possible combination of the match where no couple played in a match will be, {A, x} {C, w} & {(7, x} {A, w} , hence there are two possible combination after choosing }

n(n - l)(n - 2)(n - 3)= 5.6.7.8

So, n = 8

Hence, the number of persons will be, In = 16

──────────────────────────────────────────────────────────────────────────────────────────