A team
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Let team A = team with 6 boys and 4 girlsnahid078 wrote:A team consists of 6 boys and 4 girls and other has 5 boys and 3 girls. How many single matches can be arranged between two teams when a boy plays against a boy and a girl plays against a girl?
Let team B = team with 5 boys and 3 girls
TOTAL number of games = # of games between girls + # of games between boys
# of games between girls
Take the task of listing games and break it into stages.
Stage 1: Select girl from Team A
There are 4 girls, so we can complete stage 1 in 4 ways
Stage 2: Select girl from Team B
There are 3 girls, so we can complete stage 2 in 3 ways
By the Fundamental Counting Principle (FCP), we can complete the two stages (and thus select 2 girls to play a match) in (4)(3) ways (12 ways)
# of games between boys
Take the task of listing games and break it into stages.
Stage 1: Select boy from Team A
There are 6 boys, so we can complete stage 1 in 6 ways
Stage 2: Select boy from Team B
There are 5 boys, so we can complete stage 2 in 5 ways
By the Fundamental Counting Principle (FCP), we can complete the two stages (and thus select 2 boys to play a match) in (6)(5) ways (30 ways)
So, TOTAL number of games = 12 + 30
= 42
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Cheers,
Brent