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Permutations and Combination

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by BTGmoderatorRO » Sun Dec 24, 2017 9:43 am
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 desgnated with these codes?

A. 2 (26)^5
B. 26(26)^4
C. 27(26)^4
D. 26(26)^5
E. 27(26)^5

OA is C

What is the best approach to solving this? An Expert is needed here pls.Thanks[/spoiler]
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by elias.latour.apex » Sun Dec 24, 2017 10:28 am
Well, the number of four-letter codes is 26^4 and the number of five-letter codes is 26^5. So all you have to do is to add those numbers together.

What you need to realize is that you have:

26*(26^4) +
1*(26^4) = 27(26^4)

(A) is too big.
(B) is just another way of saying the number of five-letter codes.
(C) is what we're looking for.
both (D) and (E) are way, way too big.
Elias Latour
Verbal Specialist @ ApexGMAT
blog.apexgmat.com
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