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Permutations & Combinations

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by KItuz » Sun Oct 23, 2011 1:18 pm
A certain stock exchange designates each stock with one-, two-, or three-letter code, where each letter is selected from the 26 letters of the alphabet. If the letters may be repeated and if the same letters used in a different order constitute a different code, how many different stocks is it possible to uniquely designate with these codes?
a] 2,951
b] 8,125
c] 15,600
d] 16,302
e] 18,278

Correct ans - e any clue how?
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by neelgandham » Sun Oct 23, 2011 1:31 pm
No of one digit codes = 26
No of two digit codes = 26*26 (A*A can also be a code)
No of three digit codes = 26*26*26 ( A*A*A can also be a code)

Total # of codes = 26 + 26*26 + 26*26*26 = 18278 Option E
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by Brent@GMATPrepNow » Sun Oct 23, 2011 3:30 pm
neelgandham's is great.

I thought I'd just mention one thing about calculating 26+(26x26)+(26x26x26)
On the GMAT, the test-makers would never require us to perform these kinds of lengthy calculations, BUT it's still possible that you could be given answer choices that SUGGEST that we need to actually perform the calculations.

The answer choice here are great in that they might lead you start calculating.
However, if we focus on the units of each part, we see a faster way to arrive at the correct answer.

26 has 6 as its units digit
26^2 has 6 as its units digit
26^3 has 6 as its units digit

So, (26)+(26x26)+(26x26x26) = (26)+(___6)+(____6) = _____8

Since only E has 8 as its units digit, the answer must be E

Cheers,
Brent
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