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GMAT Prep - Combination Problem

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GMAT Prep - Combination Problem [#permalink] New post 29 Aug 2006, 16:20
Can someone please tell me how they got 18,278 as an answer - see attached image of the problem.

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 [#permalink] New post 29 Aug 2006, 18:59
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
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 [#permalink] New post 29 Aug 2006, 21:57
#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

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 [#permalink] New post 30 Aug 2006, 01:52
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.
  [#permalink] 30 Aug 2006, 01:52
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