Problem Solving

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

OA is C

Do I need a special formula to solve this? An Expert.

Roland2rule 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

OA is C

Do I need a special formula to solve this? An Expert.

Since you can use either a 4 letter symbol or a 5 letter symbol, you add the number of symbols for each.

Since the question doesn't say a letter can't be used more than once, you are free to use any of the 26 letters in each position.

So, the number of four letter symbols is 26*26*26*26 = 26^4

The number of 5 letter symbols is as above multiplied by one more 26, or 26^5.

Adding the two gives the correct answer 26^4 + 26^5. Notice that this is not among the correct answers. Don't give up hope.

Factor out the 26^4 and rewrite: 26^4(1+26) = [spoiler](26^4)*27, C[/spoiler]