Question

How many strings of length 5 are there over the alphabet { x , y , z } that either begin with z or end with z ?

Answer 1

Answer: 135

Explanation:

Given : The total number of alphabets { x , y , z } = 3

The number of possible strings when the first place is occupied by z:_

`1*3*3*3*3=3^4=81`

The number of possible strings when the last place is occupied by z:_

`3*3*3*3*1=3^4=81`

The number of possible strings when the first and the last place is occupied by z:_

`1*3*3*3*1=3^3=27`

Now, the number of possible strings where either begin with z or end with z:-

`81+81-27=135`

Hence, the number of strings of length 5 are there over the alphabet { x , y , z } that either begin with z or end with z =135