SOLUTION: In how many ways can double game of tennis be arranged from eight boys and four girls if each side must have one boy and one girl? Thanks!

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Question 568942: In how many ways can double game of tennis be arranged from eight boys and four girls if each side must have one boy and one girl?
Thanks!
Answer by Theo(13342) (Show Source):
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each side must have 1 boy and 1 girl.
this makes the number of possible teams equal to 4 * 8 = 32.
each girl can be paired with any of the 8 boys.

it takes 2 teams to play a game.
the games can be arranged in 32 * 31 / 2 = 496 ways.
32 * 31 / 2 is the combination formula of 32C2.

this would be easier to actually show what happens if there were less boys and girls.

assume there were 2 girls and 3 boys
identify the girls by the letter a and b
identify the boys by the numbers 1 and 2 and 3.
there are 2 * 3 = 6 possible teams.
those teams are
a1
a2
a3
b1
b2
b3
it takes 2 teams to play a game.
the number of possible games where each time plays each other team only once would be given by the formula 6C2 which results in 6 * 5 / 2 which results in 15 possible games.
the possible games to be arranged would be as follows:
-----
a1 plays a2
a1 plays a3
a1 plays b1
a1 plays b2
a1 plays b3
-----
a2 plays a3
a2 plays b1
a2 plays b2
a2 plays b3
-----
a3 plays b1
a3 plays b2
a3 plays b3
-----
b1 plays b2
b1 plays b3
-----
b2 plays b3
-----
the formula can be shown to be applicable with 2 girls and 3 boys.
the same formula is used with 4 girls and 8 boys to get the answer provided above.
number of possible teams if 4 * 8 = 32
number of possible games is 32C2 which is equal to 32 * 31 / 2 = 496.