Combination/permitation : GMAT Problem Solving (PS)
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# Combination/permitation

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27 Jul 2010, 12:35
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25% (medium)

Question Stats:

83% (02:01) correct 17% (00:00) wrong based on 6 sessions

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All of the stock on the over counter market are designed by either 4 letter or 5 letter code that is created by using the 26 letter of the alphabet, which of the following given is the maximum number of differnt stock that can be designed with these code

a. 2 (26)^5
b. 26(26)^4
c. 27(26)^4
d. 26(26)^5
e. 27(26)^5
[Reveal] Spoiler: OA

Last edited by whiplash2411 on 27 Jul 2010, 13:00, edited 1 time in total.
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27 Jul 2010, 13:04
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So the number of possible stocks that can be designed using the 4 letter combination are as follows:

Each space in the four letters can be filled in 26 ways. So the total = $$26^4$$

Similarly for the five letter combination: Five spaces in 26 ways each = $$26^5$$

Overall total = Sum of four and five letter stocks = $$26^4+$$$$26^5$$ = $$26^4(1+26) = 27*26^4$$

Hope this helps.
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27 Jul 2010, 13:05
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Expert's post
kilukilam wrote:
All of the stock on the over counter market are designed by either 4 letter or 5 letter code that is created by using the 26 letter of the alphabet, which of the following given is the maximum number of differnt stock that can be designed with these code

a. 2 (26)^5
b. 26(26)^4
c. 27(26)^4
d. 26(26)^5
e. 27(26)^5

4-digit code: XXXX - each digit can take 26 values (26 letters), so total # of 4-digits code possible is 26^4;
The same for 5-digit code: XXXXX - 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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28 Jul 2010, 16:09
kilukilam wrote:
All of the stock on the over counter market are designed by either 4 letter or 5 letter code that is created by using the 26 letter of the alphabet, which of the following given is the maximum number of differnt stock that can be designed with these code

a. 2 (26)^5
b. 26(26)^4
c. 27(26)^4
d. 26(26)^5
e. 27(26)^5

We can consider the combination of 4 letter codes or 5 letter codes as a 5 letter code which can have an empty first letter.
The first letter of the code can be filled in 27 ways (26 ways for the alphabet +1 for empty letter)
Rest 4 letters of the code can be filled in 26^4 ways.
So the maximum no of codes possible is 27 (26)^4
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16 May 2011, 21:26
Step 1:

The number of codes that can be generated using 4-letters are 26^4

Step 2:
The number of codes that can be generated using 5-letters are 26^5

Step 3:

The total numbers of codes that can be generated using 4-letters and 5-letters are

⇨ 26^4+26^5
⇨ 26^4(1+26)
⇨ (26^4)*27

So, the answer is (C).
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17 May 2011, 03:07

26*26*26*26 + 26*26*26*26*26
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17 May 2011, 08:07
26^4 + 26^5

26^4(26+1)

C
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Re: Combination/permitation   [#permalink] 17 May 2011, 08:07
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# Combination/permitation

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