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)5B. 26(26)426(26)4C. 27(26)427(26)4D. 26(26)526(26)5E. 27(26)5

Answer 1

The correct option is
`27(26)^4`.

Explanation:

Consider the provided information.

market are designated by either a 4 letter or a 5 letter code that is created by using the 26 letters of the alphabet.

Case I:

The number of ways to select a 4 letter.

For 1st letter we have 26 choices.

For 2nd letter we have 26 choices.

Similarly for 3rd and 4th digit we have 26 choices.

Thus, the number of ways are:
`26*26*26*26=26^4`

Case II:

The number of ways to select a 5 letter.

For 1st letter we have 26 choices.

For 2nd letter we have 26 choices.

Similarly for 3rd, 4th and 5th digit we have 26 choices.

Thus, the number of ways are:
`26*26*26*26*26=26^5`

Hence, the total number of ways are:
`26^4+26^5=26^4(1+26)=27(26)^4`

Thus, the correct option is
`27(26)^4`.