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

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Question 1168171: In how many ways can a doubles game of tennis be arranged from seven boys and five girls if each side must have one boy and one girl?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

The first team (boy,girl) can be arranged in 7*5 = 35 ways.


After that, the second team (boy,girl) can be arranged in 6*4 = 24 ways.


Such teams can be combined in   = 35*12 = 420 different ways for a game.    ANSWER

Solved.


Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


Probability is an area of mathematics where it is useful to know different methods for solving a problem.

Here is an alternative to the (perfectly good) method shown by the other tutor.

(1) Choose 2 of the 7 boys in C(7,2) = 21 ways
(2) Choose 2 of the 5 girls in C(5,2) = 10 ways
(3) Make 2 teams each with one boy and one girl in 2 ways

ANSWER: 21*10*2 = 420 ways.
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