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nahid078: Master | Next Rank: 500 Posts; Posts: 105; Joined: Tue May 13, 2014 10:41 amFollowed by: 1 member; Thanked: 2 times

by nahid078 » Wed Jul 01, 2015 8:13 am

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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?

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Source: Beat The GMAT — Problem Solving | Wed Jul 01, 2015 8:13 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Jul 01, 2015 9:14 am

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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