Question

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 designated with these codes?
A. 2(26)52(26)5

B. 26(26)426(26)4

C. 27(26)427(26)4

D. 26(26)526(26)5

E. 27(26)5

Answer 1

Answer:

C. $27(26)^{4}$

Step-by-step explanation:

The stocks can be coded using either 4 letters or 5 letters.

Maximum possibilities for 4 letter codes:

Since any letter from 26 alphabets can be used, there are 26 ways to chose each of the 4 letters of the code.

Therefore, total number of ways to form the code will be = 26 x 26 x 26 x 26 = $26^{4}$

Maximum possibilities for 5 letter codes:

Based on the same logic as used in previous part, there are 26 ways to chose each of the 5 letters of the code.

So, total number of ways to form the code will be = 26 x 26 x 26 x 26 x 26 = $26^{5}$

Total maximum possible ways to code:

The total maximum possible codes will be the sum of possible 4 digit and 5 digit codes.

So, maximum number of codes = $26^{4}+26^{5}=26^{4}(1+26) = 27(26)^{4}$

Therefore, option C gives the correct answer of maximum number of different stocks that can be designated with these codes.