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Combinations of 4-letter and 5-letter codes

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Combinations of 4-letter and 5-letter codes [#permalink]  16 Nov 2011, 20:18
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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?

1. 2(26^5)
2. 26(26^4)
3. 27(26^4)
4. 26(26^5)
5. 27(26^5)
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Re: Combinations of 4-letter and 5-letter codes [#permalink]  16 Nov 2011, 21:21
Number of 4-letter codes: 26 * 26 * 26 * 26 = 26^4
Number of 5-letter codes: 26 * 26 * 26 * 26 * 26 = 26^5

Total Number of codes: 26^4 + 26^5 = 26^4 + 26*(26^4) = 27*(26^4)

Therefore, the answer is C: 27*(26^4).
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Re: Combinations of 4-letter and 5-letter codes [#permalink]  17 Nov 2011, 07:01
26^4+26^5 = 26^4(1+26) = 27(26^4) C
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Re: Combinations of 4-letter and 5-letter codes   [#permalink] 17 Nov 2011, 07:01
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