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armaan700+: Senior | Next Rank: 100 Posts; Posts: 75; Joined: Sun Jun 14, 2009 1:41 am; Location: india; Thanked: 2 times; Followed by:1 members

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by armaan700+ » Tue Jan 26, 2010 10:06 am

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There are 3 red chips and 2 blue ones.
When arranged in a row, they form a certain color pattern, for example RBRRB. How many color patterns?

10
12
24
60
100

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Source: Beat The GMAT — Problem Solving | Tue Jan 26, 2010 10:06 am

thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 am; Thanked: 137 times; Followed by:5 members

by thephoenix » Tue Jan 26, 2010 10:33 am

= 5!/3!2!
= 10

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sat Sep 21, 2019 11:09 am

armaan700+ wrote:There are 3 red chips and 2 blue ones.
When arranged in a row, they form a certain color pattern, for example RBRRB. How many color patterns?

10
12
24
60
100

The number of possible patterns is 5! / (3!*2!) = (5 x 4) / 2 = 10.

Alternate Solution:

Note that if the 5 chips were all of different colors, then we would have 5! = 120 different arrangements. But because there are 3 identical red chips and 2 identical blue chips, we must reduce the number of possible arrangements, using the indistinguishable permutations formula, obtaining 5! / (3!*2!) = (5x4) / (2x1) = 10.

Answer: A

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