permutation

[smallsorrow]

All of the stocks on the Over-the-counter maket are designated by either a 4-letter or a five letter code that is created by using the alphabet. Which of the following gives the maximum number of different stocks that can be designated with these codes?
A)2(26^5)
B)26(26^4)
c)27(26^4)
D)26(26^5)
E)27(26^5)

my thought was:
4(26)/4! + 5(26)/5! (but no factorials required - why?)

[parallel_chase]

All of the stocks on the Over-the-counter maket are designated by either a 4-letter or a five letter code that is created by using the alphabet. Which of the following gives the maximum number of different stocks that can be designated with these codes?
A)2(26^5)
B)26(26^4)
c)27(26^4)
D)26(26^5)
E)27(26^5)

my thought was:
4(26)/4! + 5(26)/5! (but no factorials required - why?)

factorial would be required if the question had stated that none of the alphabets can be repeated.

even then the i dont think factorial would be needed
if alphabets cannot be repeated

4 letter code : 26 * 25 * 24 * 23

Since letters can be repeated

4 letter code : 26*26*26*26 = 26^4
5 letter code : 26*26*26*26*26 = 26^5

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

Hope this helps.

[mbaapplicant2008]

Thanks, parallel_chase