Combinations

[gmatgirl12]

All of the stocks on the over the counter market are designed by either a 4 letter of a 5 letter code that is created by using 26 letters of 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)

[BuckeyeT]

So, the code can be either 4-digit or 5-digit. Each digit can be one of 26 values. And, the values are not dependant on each other.

So,
4-digit = 26*26*26*26 = 26^4
5-digit = 26*26*26*26*26 = 26^5

4-digit options + 5-digit options:
26^4 + 26^5
Factor out 26^4
26^4 (1 + 26)
26^4 (27)

C.