Find the number of ways 5 boys and 4 girls can be seated in a row.
2 girls cannot sit together
Answer option was 43200
2 girls cannot sit together
Answer option was 43200
Take the task of seating the 9 children and break it into stages.s91arvindh wrote:Find the number of ways 5 boys and 4 girls can be seated in a row.
2 girls cannot sit together
Stage 1: Arrange the 5 boys in a row (in 5 ADJACENT chairs)
There's a nice rule that says we can arrange n unique objects in a row in n! ways.
So, we can complete stage 1 in 5! ways (120 ways)
IMPORTANT: Now place a chair on either side of each boy to get:
_B_B_B_B_B_
These are the "girl chairs" Notice that this ENSURES that no two girls sit together.
Stage 2: Seat one of the girls
There are 6 chairs, so we can complete this stage in 6 ways.
Stage 3: Seat another girl
There are now 5 chairs remaining digits, so we can complete this stage in 5 ways.
Stage 4: Seat another girl
There are now 4 chairs remaining digits, so we can complete this stage in 4 ways.
Stage 5: Seat the last girl
There are now 3 chairs remaining digits, so we can complete this stage in 3 ways.
By the Fundamental Counting Principle (FCP), we can complete all 5 stages (and thus seat all 9 children) in (120)(6)(5)(4)(3) ways ([spoiler]= 43,200 ways[/spoiler])
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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
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MEDIUM
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DIFFICULT
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Cheers,
Brent
