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permutation

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by smallsorrow » Sun Oct 12, 2008 9:20 am
All of the stocks on the Over-the-counter maket are designated by either a 4-letter or a five letter code that is created by using 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)

my thought was:
4(26)/4! + 5(26)/5! (but no factorials required - why?)
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Re: permutation

by parallel_chase » Sun Oct 12, 2008 9:27 am
smallsorrow wrote:All of the stocks on the Over-the-counter maket are designated by either a 4-letter or a five letter code that is created by using 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)

my thought was:
4(26)/4! + 5(26)/5! (but no factorials required - why?)
factorial would be required if the question had stated that none of the alphabets can be repeated.

even then the i dont think factorial would be needed
if alphabets cannot be repeated

4 letter code : 26 * 25 * 24 * 23

Since letters can be repeated

4 letter code : 26*26*26*26 = 26^4
5 letter code : 26*26*26*26*26 = 26^5

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

Hope this helps.
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by mbaapplicant2008 » Thu Oct 30, 2008 1:25 am
Thanks, parallel_chase
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