nahid078 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 A = team with 6 boys and 4 girls
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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Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. For more information about the FCP, watch our free video: https://www.gmatprepnow.com/module/gmat-counting?id=775

Then you can try solving the following questions:

EASY
- https://www.beatthegmat.com/what-should- ... 67256.html
- https://www.beatthegmat.com/counting-pro ... 44302.html
- https://www.beatthegmat.com/picking-a-5- ... 73110.html
- https://www.beatthegmat.com/permutation- ... 57412.html
- https://www.beatthegmat.com/simple-one-t270061.html
- https://www.beatthegmat.com/mouse-pellets-t274303.html


MEDIUM
- https://www.beatthegmat.com/combinatoric ... 73194.html
- https://www.beatthegmat.com/arabian-hors ... 50703.html
- https://www.beatthegmat.com/sub-sets-pro ... 73337.html
- https://www.beatthegmat.com/combinatoric ... 73180.html
- https://www.beatthegmat.com/digits-numbers-t270127.html
- https://www.beatthegmat.com/doubt-on-sep ... 71047.html
- https://www.beatthegmat.com/combinatoric ... 67079.html


DIFFICULT
- https://www.beatthegmat.com/wonderful-p- ... 71001.html
- https://www.beatthegmat.com/ps-counting-t273659.html
- https://www.beatthegmat.com/permutation- ... 73915.html
- https://www.beatthegmat.com/please-solve ... 71499.html
- https://www.beatthegmat.com/no-two-ladie ... 75661.html
- https://www.beatthegmat.com/laniera-s-co ... 15764.html

Cheers,
Brent