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# All of the stock on the over counter market are designed by either 4

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All of the stock on the over counter market are designed by either 4 [#permalink]

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27 Jul 2010, 13:35
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25% (medium)

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76% (01:26) correct 24% (01:38) wrong based on 72 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 different 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 Bunuel on 13 Apr 2017, 01:28, edited 2 times in total.
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Re: All of the stock on the over counter market are designed by either 4 [#permalink]

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27 Jul 2010, 14:04
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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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Re: All of the stock on the over counter market are designed by either 4 [#permalink]

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27 Jul 2010, 14:05
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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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Re: All of the stock on the over counter market are designed by either 4 [#permalink]

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28 Jul 2010, 17:09
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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Re: All of the stock on the over counter market are designed by either 4 [#permalink]

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16 May 2011, 22:26
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

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Re: All of the stock on the over counter market are designed by either 4 [#permalink]

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17 May 2011, 04:07

26*26*26*26 + 26*26*26*26*26
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Re: All of the stock on the over counter market are designed by either 4 [#permalink]

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17 May 2011, 09:07
26^4 + 26^5

26^4(26+1)

C
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Re: All of the stock on the over counter market are designed by either 4 [#permalink]

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27 May 2017, 07:10
Expert's post
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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 different 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

1. The maximum is when alphabets are repeating and ordering is important, which is n^r
2. For 4 letter codes it is 26^4
3. for 5 letter codes it is 26^5
4. Total is (26^4 + 26^5)= 26^4(1+26) = 27(26)^4
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Re: All of the stock on the over counter market are designed by either 4 [#permalink]

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31 May 2017, 11:23
amit2k9 wrote:
26^4 + 26^5

26^4(26+1)

C

Can someone explain the step where we get (26 + 1). I follow up until that point. Unsure how we get that part.

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Re: All of the stock on the over counter market are designed by either 4 [#permalink]

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31 May 2017, 12:27
leeum wrote:
amit2k9 wrote:
26^4 + 26^5

26^4(26+1)

C

Can someone explain the step where we get (26 + 1). I follow up until that point. Unsure how we get that part.

That's done by factoring out 26^4 from both terms:

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

Hope it's clear.
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Re: All of the stock on the over counter market are designed by either 4 [#permalink]

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05 Jun 2017, 16:11
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 different 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 need to determine the maximum number of different stocks that can be designated by a 4-letter or 5-letter code that is created by using the 26 letters of the alphabet. Number of 5-letter codes:

26 x 26 x 26 x 26 x 26 = 26^5

Number of 4-letter codes:

26 x 26 x 26 x 26 = 26^4

Since the stocks can be designated by a 4-letter OR 5-letter code, we must add our results together to determine the maximum number of codes that can be created.

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

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Re: All of the stock on the over counter market are designed by either 4   [#permalink] 05 Jun 2017, 16:11
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