For the alphabet a b c d e f g how many strings in 8 have a

For the alphabet = {a, b, c, d, e, f, g}, how many strings in ⁸ have at least one pair of consecutive identical letters?

Solution

Sol:

Given alphabet = {a, b, c, d, e, f, g}

The total number of bit strings of length 8 are 2^8 = 256

We subtract from the total number of bit strings of length 8 those that have only 0 pair of consecutive identical letters:

i.e. 2^8 - [C(8,0)] = 256 - 1 =255

Therefore, total number of strings are 255.