SOLUTION: In how many ways can a doubles game of tennis be arranged from eleven boys and seven girls if each side must have one boy and one girl?

Algebra ->  Permutations -> SOLUTION: In how many ways can a doubles game of tennis be arranged from eleven boys and seven girls if each side must have one boy and one girl?       Log On


   

Question 1022435: In how many ways can a doubles game of tennis be arranged from eleven boys and seven girls if each side must have one boy and one girl?
Answer by mathmate(429) About Me  (Show Source):
You can put this solution on YOUR website!

Question:
In how many ways can a doubles game of tennis be arranged from eleven boys and seven girls if each side must have one boy and one girl?

Solution:
It should be understood that order does not count here, so it is a question of combination.
For each match, we need two boys and two girls.
The number of ways this can be done is C(11,2)*C(7,2)=55*21=1155
where C(n,r)=n!/(r!(n-r)!) is the binomial coefficient.

Moreover, given two boys and two girls, there are two arrangements of opponents, i.e. a particular girl can choose one of the two boys as partner.

Therefore the total number of different matches is 1155*2=2310.