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# All the stocks on the over-the-counter market are designated

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Schools: Kellogg; Ross ($$); Tuck Followers: 2 Kudos [?]: 32 [0], given: 6 Re: GMATPrep Permutations [#permalink] ### Show Tags 02 Sep 2009, 12:27 for the four letter code: 26^4 for the five letter code: 26^5 add them up 26^4(1+26) = 27(26^4) Intern Joined: 30 Jun 2009 Posts: 48 Followers: 1 Kudos [?]: 9 [0], given: 2 Re: GMATPrep Permutations [#permalink] ### Show Tags 03 Sep 2009, 07:40 madeinafrica wrote: for the four letter code: 26^4 for the five letter code: 26^5 add them up 26^4(1+26) = 27(26^4) CAn you please elaborate your answer? Current Student Affiliations: ? Joined: 20 Jul 2009 Posts: 191 Location: Africa/Europe Schools: Kellogg; Ross ($$); Tuck
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03 Sep 2009, 07:59
To have the four letters code, you have to pick four letters from 26.
since it's a code, you can have AAAA, or AAAM etc..

first place you'll have 26 choices, second place, 26 choices again. thus you have $$26^4$$ at the end.

Same for the five letter code. you will have $$26^5$$ (possible to have BBBBB or BBBBA as a code)

then you add them up: $$26^4 + 26^5 =26^4 (1+26)$$

hope it's ok.
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03 Sep 2009, 08:32
To have the four letters code, you have to pick four letters from 26.
since it's a code, you can have AAAA, or AAAM etc..

first place you'll have 26 choices, second place, 26 choices again. thus you have $$26^4$$ at the end.

Same for the five letter code. you will have $$26^5$$ (possible to have BBBBB or BBBBA as a code)

then you add them up: $$26^4 + 26^5 =26^4 (1+26)$$

hope it's ok.

Got that part, the tricky thing that I am missing is this 26^4 (1+26) equals solution D
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22 Dec 2010, 00:40
Please, help me to rewrite the question. It is too obscure to see.
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22 Dec 2010, 00:58
Expert's post
thangvietnam wrote:
Please, help me to rewrite the question. It is too obscure to see.

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

In 4-digit code {XXXX} each digit can take 26 values (as there are 26 letters), so total # of 4-digits code possible is 26^4;

The same for 5-digit code {XXXXX} again each digit can take 26 values (26 letters), so total # of 5-digits code possible is 26^5;

Total: $$26^4+26^5=26^4(1+26)=27*26^4$$.

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25 Apr 2011, 17:15
the letters can be reused as there are no restriction on this.

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

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26 Apr 2011, 06:21
Total = 4-letter + 5-letter

= 26^4 + 26^5

= 26^4(1+26)

= 27(26^4)

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26 Apr 2011, 07:22
This is asking for possible combinations in 4-letter and 5-letter.

How many 4-letter coded stocks: 26 x 26 x 26 x 26 = 26^4
How many 5-letter coded stocks: 26 x26 x 26 x 26 x 26 = 26^5

Maximum is having all the 4-letter and all 5letter combo:
=26^4 + 26^5
=26^4(1 + 26^1)
=26^4(27)

C
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03 May 2011, 04:55
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03 May 2011, 10:54
note 1-- it doesn't say that 4 code or 5 code has to be distinct alphabets...

So 4 codes can be arranged as (26)^4 ways
and 5 letters code as (26)^5 ways

Since it is either (26)^4+(26)^5 = (26)^4 (1+26)
= 27 (26)^4

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03 May 2011, 20:47
straight C it is.
26^4 ( 26 + 1).

for 4 letters permutation is 26 * 26* 26 * 26. Similarly for 5 letters too.
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Re: GMATPrep Permutations   [#permalink] 03 May 2011, 20:47

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