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All of the stocks on the over the counter market are designated by eit

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Shbm
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Re: All of the stocks on the over the counter market are designated by eit [#permalink] New post   01 Aug 2018, 22:28
Bunuel wrote:
Shbm wrote:
Bunuel wrote:
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.




I used the 26c4 multipled 26c5 and got the answer wrong. Whats the reason for this and when should we use this formula?


26C4 gives the number of unordered groups of 4 different letters out of 26. For one, the order matters, {a, b, c, d} code is different from {b, a, c, d} code. Also, the letters could be repeated in the code, and 26C4 gives groups of 4 different letters. Finally, multiplying is wrong because 4-letter codes and 5-letter codes are different cases, so the number of possible codes should be added not multiplied.

Hope it's clear.




thanks bossman. are these type of questions generally placed in the 700 level category or can be a product of the 600-700 level?
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Re: All of the stocks on the over the counter market are designated by eit [#permalink] New post   08 Dec 2019, 20:12
Would someone PLEASE explain why:

26^4+26^5 is EQUAL TO 26^4(1+26)??? I don't understand!
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Re: All of the stocks on the over the counter market are designated by eit [#permalink] New post   18 Dec 2020, 23:09
Wouldn't we be including all the 4 digit code again when we do 27(26⁴)
Instead shouldn't it be 26(26⁴)?

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Re: All of the stocks on the over the counter market are designated by eit [#permalink] New post   29 Sep 2021, 00:00
Hello experts
Bunuel, VeritasKarishma, chetan2u, scott Woodbury-Stewart

Can you please explain?
Why we are repeating the same letters even we want different codes and why not 26*25*24*23+26*25*24*23*22?

Thanks in advance
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Re: All of the stocks on the over the counter market are designated by eit [#permalink] New post   29 Sep 2021, 01:55
Here i am taking 3 letters( A, B, C) to make 3 letter code.
possible 3 letter codes are

AAA
ABB
ACC
AAC
AAB
ABC
ACB
ABA
ACA

BBB
BAA
BCC
BBA
BBC
BAC
BCA
BCB
BAB

CCC
CBB
CAA
CBA
CAB
CCA
CCB
CAC
CBC

total 9+9+9=27 possible codes( 3*3*3=27)
chetan2u, Bunuel can we apply same analogy to the above problem as well?

Thanks
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Re: All of the stocks on the over the counter market are designated by eit [#permalink] New post   29 Sep 2021, 02:25
Expert Reply
kadamhari825 wrote:
Here i am taking 3 letters( A, B, C) to make 3 letter code.
possible 3 letter codes are

AAA
ABB
ACC
AAC
AAB
ABC
ACB
ABA
ACA

BBB
BAA
BCC
BBA
BBC
BAC
BCA
BCB
BAB

CCC
CBB
CAA
CBA
CAB
CCA
CCB
CAC
CBC

total 9+9+9=27 possible codes( 3*3*3=27)
chetan2u, Bunuel can we apply same analogy to the above problem as well?

Thanks



Yes, that is correct.
Each place: any of three so 3*3*3
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Re: All of the stocks on the over the counter market are designated by eit [#permalink] New post   24 Oct 2023, 10:50
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Re: All of the stocks on the over the counter market are designated by eit [#permalink]
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