Answer: 135
Step-by-step explanation:
Given : The total number of alphabets { x , y , z } = 3
The number of possible strings when the first place is occupied by z:_
[tex]1\times3\times3\times3\times3=3^4=81[/tex]
The number of possible strings when the last place is occupied by z:_
[tex]3\times3\times3\times3\times1=3^4=81[/tex]
The number of possible strings when the first and the last place is occupied by z:_
[tex]1\times3\times3\times3\times1=3^3=27[/tex]
Now, the number of possible strings where either begin with z or end with z:-
[tex]81+81-27=135[/tex]
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
