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# GMAT Prep - Combination Problem

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Intern
Joined: 25 Aug 2006
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GMAT Prep - Combination Problem [#permalink]  29 Aug 2006, 15:20
Can someone please tell me how they got 18,278 as an answer - see attached image of the problem.

AP
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File comment: Combinatoin Problem

gmatprep_problem10jpg.jpg [ 38.44 KiB | Viewed 459 times ]

Manager
Joined: 26 Aug 2006
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1) possibilities for one letter - 26
2) possibilities for two letters - 26*26 = 676
3) possibilities for three letters - 26*26*26 = 17576

Total possibilities = 26+676+17576 = 18278
Manager
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#of ways of selecting 1 digit code = 26
#of ways of selecting 2 digit code = 26^2(since digits can be repeated)
#of ways of selecting 3 digit code = 26^3(since digits can be repeated)

Total # of ways= 26+26^2+26^3
=26(1+26+26^2)
=26(703)
=18278

Hence E

Heman
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Same method. Trick to this one is the to read the problem carefully. It says that the letters CAN be repeated. I think your answer choice would be something like 26+ (26*25) + (26*25*24), which is correct only if the letters CANNOT be repeated.
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