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(26^5)b) 26(26^4)c) 27(26^4)d) 26(26^5)e) 27(26^5)

Answer 1

Answer: e)
`27(26^5)`

Explanation:

Given : 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.

The number of ways to make a 4-letter code ( If repetition of letters is allowed) =
`26*26*26*26=(26)^4`

Similarly, The number of ways to make a 5-letter code =

`26*26*26*26*26=(26)^5`

Now, the combined number of ways to make either a 4-letter or a 5-letter code :-

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

Hence, the correct answer is e)
`27(26^5)`.