Question

How many strings of length 10 over the αbet a, b, c, d have at least one 'b' somewhere in the string?

a) 4^10
b) 3^10
c) 4^10-3^10
d) none of the above

Answer 1

The number of strings of length 10 using the alphabet a, b, c, and d that contain at least one 'b' is calculated by subtracting the total number of strings that can be made without using 'b' (3^10) from the total number of all possible strings (4^10), resulting in 4^10 - 3^10.

Step-by-step explanation:

The question asks about the number of strings of length 10 using the alphabet a, b, c, and d that contain at least one 'b'. To solve this, we utilize the principle of complementation.

The total number of possible strings without any restriction is 4^10. However, we want to exclude those strings that do not contain 'b', which can be formed with the remaining three letters (a, c, d), thus giving us 3^10 strings without any 'b'. To find the number of strings with at least one 'b', we subtract the number of strings without 'b' from the total number of strings.

Therefore, the answer to the question is 4^10 - 3^10.