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

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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

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