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

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Re: GMATPrep Permutations [#permalink] New post 02 Sep 2009, 11:27
for the four letter code: 26^4
for the five letter code: 26^5

add them up 26^4(1+26) = 27(26^4)
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Re: GMATPrep Permutations [#permalink] New post 03 Sep 2009, 06:40
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?
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Re: GMATPrep Permutations [#permalink] New post 03 Sep 2009, 06:59
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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Re: GMATPrep Permutations [#permalink] New post 03 Sep 2009, 07:32
madeinafrica wrote:
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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Re: GMATPrep Permutations [#permalink] New post 21 Dec 2010, 23:40
Please, help me to rewrite the question. It is too obscure to see.
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Re: GMATPrep Permutations [#permalink] New post 21 Dec 2010, 23:58
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.

Answer: C.
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Re: GMATPrep Permutations [#permalink] New post 25 Apr 2011, 16:15
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)

Answer is C.
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Re: GMATPrep Permutations [#permalink] New post 26 Apr 2011, 05:21
Total = 4-letter + 5-letter

= 26^4 + 26^5

= 26^4(1+26)

= 27(26^4)

Answer - C
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Re: GMATPrep Permutations [#permalink] New post 26 Apr 2011, 06:22
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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Code number [#permalink] New post 03 May 2011, 03:55
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Re: Code number [#permalink] New post 03 May 2011, 09:54
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

Answer is C.
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Re: GMATPrep Permutations [#permalink] New post 03 May 2011, 19:47
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, 19:47
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