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All of the stocks on the over the counter market

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by ska7945 » Wed Sep 10, 2008 8:13 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?

1.2(26^5)
2.26(26^4)
3.27(26^4)
4.26(26^5)
5.27(26^5)
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by schumi_gmat » Wed Sep 10, 2008 8:58 am
IMO C

4 letter code are chosen in 26^4 and 5 letter in 26^5

hence maximum way to have 4 letter or 5 letter code = 26^4 + 26^5
= 27(26^4)
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by djkvakin » Mon Dec 28, 2009 7:35 pm
Wouldn't 4 letter code be driven by the formula : 26c4? 26!/4!(26-4)! ?

and 5 letter code: 26c5: 26!/5!(26-5)! ?

What is wrong with my approach?
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by ace_gre » Mon Dec 28, 2009 10:00 pm
In this problem, the ordering of the letters matter. Hence this is a permutation problem and not combination.

For eg. consider letters A,B,C and D.
No. of unique ways of arranging 4 letters is 4*3*2*1=24. Not 4C2.

Since repetition is allowed, ans= (26^4) + (26^5) = 26^4(1 + 26)= 27 ( 26 ^4)
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