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All of the stocks on the over-the-counter market are

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Senior Manager
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All of the stocks on the over-the-counter market are [#permalink] New post 20 Jan 2007, 23:14
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All of the stocks on the over-the-counter market are designated by either a 4-letter or a 5-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be designated with these codes?
(A) 2(26^5)
(B) 26(26^4)
(C) 27(26^4)
(D) 26(26^5)
(E) 27(26^5)
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 [#permalink] New post 21 Jan 2007, 03:11
4-letter codes: 26^4
5-letter codes: 26^5

Total = 26^4 + 26^5 = 26^4(1 + 26) = 26^4(27)

Answer is (C)
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 [#permalink] New post 22 Jan 2007, 10:23
The reason why I got this wrong is because I tried to apply the formula for combinations using: n! / (r!)(n-r)!.

Can you explain the approach you used so I understand what concept I am missing?
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 [#permalink] New post 22 Jan 2007, 17:28
The combination formula does not take ordering into consideration. So AAAC , AACA, ACAA, and CAAA are counted as one.
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  [#permalink] 22 Jan 2007, 17:28
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All of the stocks on the over-the-counter market are

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