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# There are 3 red chips and 2 blue ones. When arranged in a

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Senior Manager
Joined: 22 Dec 2009
Posts: 356

Kudos [?]: 418 [1], given: 47

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14 Feb 2010, 10:06
1
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bmwhype2 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

$$\frac{5!}{3! * 2!} = 10$$ ... A
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Kudos [?]: 418 [1], given: 47

Manager
Joined: 02 Jan 2010
Posts: 132

Kudos [?]: 6 [0], given: 3

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08 Sep 2010, 03:53
bmwhype2 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

This could be put in a format RRRBB. So total ways of choosing is 5! and since there are 3 R and 2 B, putting the R/B differently within each color pattern does not change anything so we need to remove them. So the formula is 5!/(3!2!) = 10

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Great Lakes Institute of Management
http://greatlakes.edu.in

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Intern
Joined: 24 Feb 2012
Posts: 32

Kudos [?]: 19 [0], given: 18

Re: There are 3 red chips and 2 blue ones. When arranged in a [#permalink]

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24 Feb 2012, 13:07
Using MGMAT's anagram technique, ATLANTA is can be rearranged $$\frac{7!}{(3!)(2!)}$$ ways....coz of 3As and 2Ts.
Applying the same technique here:
RRRBB can be arranged in $$\frac{5!}{(3!)(2!)}$$ ways
=10

Kudos [?]: 19 [0], given: 18

Intern
Joined: 24 May 2012
Posts: 13

Kudos [?]: 1 [0], given: 1

Concentration: Entrepreneurship, International Business
Re: There are 3 red chips and 2 blue ones. When arranged in a [#permalink]

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06 Jun 2012, 11:25
Answer would be 5!/2!3!
5! for the permutation of number of ways it can be arranged. 2! and 3! for similar arrangements of Red and Black chips as no distinction factor between chips is mentioned i.e. all Red chips are identical and all black chips are identical too.

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Joined: 02 Apr 2012
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Location: United States (VA)
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Re: There are 3 red chips and 2 blue ones. When arranged in a [#permalink]

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09 Jul 2013, 15:53

$$C^5_2 * C^3_3 = 10$$

The 2 blue placed from the slot 1 to 5 and the remaining 3 placed in the rest 3 slots.
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Math Expert
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Re: There are 3 red chips and 2 blue ones. When arranged in a [#permalink]

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09 Jul 2013, 16:12

Kudos [?]: 132642 [0], given: 12326

Re: There are 3 red chips and 2 blue ones. When arranged in a   [#permalink] 09 Jul 2013, 16:12

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# There are 3 red chips and 2 blue ones. When arranged in a

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