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permutations :S [#permalink] New post 16 Jun 2009, 08:27
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33% (02:46) correct 66% (00:00) wrong based on 3 sessions
A certain stock exchange designates each stock with one-, two-, or three-letter code, where each letter is selected from the 26 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
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Re: permutations :S [#permalink] New post 16 Jun 2009, 09:10
Jozu wrote:
A certain stock exchange designates each stock with one-, two-, or three-letter code, where each letter is selected from the 26 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


stock with one-- 26
two-, 26*25= 650
or three-letter code, 26*25*24= 15,600

the total is 16,276 ... your option (d) is 16,302 thats intriguingly 26 more than my answer ... now i am probably doing something wrong but i can't figure it out and if you do, do post here b/c i am sort of curious now.
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Re: permutations :S [#permalink] New post 16 Jun 2009, 09:18
Given that each letter in each stock code can be repeated we need to factor that in our calculations:

\text {No of 1 letter codes} = 26

\text {No of 2 letter codes} = 26\times 26 = 26^2

\text {No of 3 letter codes} = 26\times 26\times 26 = 26^3

\text {Total number of codes} = 26 + 26^2 + 26^3 = 18,278

The answer is E.

For the last step there is a faster way to get the answer than doing all the multiplication.

26 has 6 in the units digit.
Also 26^2 should have 6 in the units digit.
Similarly 26^3 should have 6 in the units digit.

If you add the units digits of the three it is 18 that would mean 8 would be in the units digit of the final answer and there is only one answer choice with 8 in the units digit i.e. E

See the following thread for more on last digit of a power.

last-digit-of-a-power-70624.html#p521012
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Re: permutations :S [#permalink] New post 16 Jun 2009, 18:03
OA is E.

I'm a little confused here regarding permutations.

How do we know when to use nPr (order is relevant), nCr (order is not relevant) and your method above? I just can't seem to apply them correctly when I encounter such problems.
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Re: permutations :S [#permalink] New post 16 Jun 2009, 20:33
This problem is testing the fundamental counting principal.

Here is a link to understand it better with some examples.

http://www.wtamu.edu/academic/anns/mps/ ... _count.htm

Also checkout this thread for more on Permutations and Combinations.

permutations-combinations-help-is-on-the-way-10838.html
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Re: permutations :S [#permalink] New post 17 Jun 2009, 00:28
And of course the Walker's thread that is stickied in this forum: combinations-permutations-and-probability-references-56486.html
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Re: permutations :S   [#permalink] 17 Jun 2009, 00:28
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