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# Q13: How many different 6-letter sequences are there that

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SVP
Joined: 28 May 2005
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Q13: How many different 6-letter sequences are there that [#permalink]  22 Oct 2005, 05:00
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Q13:
How many different 6-letter sequences are there that consist of 1 A, 2 Bâ€™s, and 3 Câ€™s ?
A. 6
B. 60
C. 120
D. 360
E. 720
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hey ya......

SVP
Joined: 28 May 2005
Posts: 1743
Location: Dhaka
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Kudos [?]: 71 [0], given: 0

are both the method correct or one is wrong?
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hey ya......

Director
Joined: 21 Aug 2005
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nakib77, both are correct.
1) Consider each letter seperately,
- There is 1 A, we have 6 places to put this in - 6C1
- There are 2 B's, we have 5 places for this - 5C2
- There are 3 C's, we have 3 places - 3C3
Total possible = 6C1*5C2*3C3 = 6*10*1 = 60 ways

2) Consider all the letters together,
Total possible arrangement for 6 unique letters - 6!
Since all are not unique here - We have 3 C's and 2 B's,
It is 6!/2!3!
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