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by rkhicha » Thu Jul 15, 2010 5:16 am
All of the stocks on the OTC market are designated by either a 4-letter or a 5-letter code that is created using 26 letters of the english alphabets. Which of the following gives the maximum number of stocks that can be designated with these codes?

1. 2 (26^5)
2. 26 (26^4)
3. 27 (26^4)
4. 26 (26^5)
5. 27 (26^5)

Thanks.

OA: C
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by amising6 » Thu Jul 15, 2010 5:19 am
rkhicha wrote:All of the stocks on the OTC market are designated by either a 4-letter or a 5-letter code that is created using 26 letters of the english alphabets. Which of the following gives the maximum number of stocks that can be designated with these codes?

1. 2 (26^5)
2. 26 (26^4)
3. 27 (26^4)
4. 26 (26^5)
5. 27 (26^5)

Thanks.

OA: C
stock designated by 4 letter
- - - -
first position can be filled in 26 ways (26 alphabet)
second position can be filled in 26 ways (26 alphabet)
third position can be filled in 26 ways (26 alphabet)

fourth position can be filled in 26 ways (26 alphabet)
so total number of ways four 4 letter code
26*26*26*26
similirly for 5 letter code
26*26*26*26*26
so total number of ways
26^4+26^5
26^4(1_26)
26^4*27
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by Rahul@gurome » Thu Jul 15, 2010 5:22 am
A 4-letter code can be chosen 26^4 ways.
A 5-letter code can be chosen 26^5 ways.

Therefore, maximum number of stocks that can be designated with these codes = 26^4 + 26^5 = 26^4(1 + 26)
= 27 (26^4)

[spoiler]The correct answer is (C).[/spoiler]
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