String of 8 letters of the alphabet with repeated letters al

String of 8 letters of the alphabet with repeated letters allowed. How many words are there? How many words end with the letter T? How many words begin with R and end with Y? How many words start with A or B? How many words begin with A or end with B? Please explain. Thanks.

Solution

String of 8 letters of the alphabet with repeated letters allowed. How many words are there? How many words end with the letter T? How many words begin with R and end with Y? How many words start with A or B? How many words begin with A or end with B? Please explain.

How many words are there?
Ans :
Each letter can be filled in 26 ways
So, 8 letters --> 26*26* .. 8 times ---> 26^8 possibilities

How many words end with the letter T?
Ans :
Ending letter = T
Other 7 letters ---> 26^7 ways
So, total we have 26^7 possibilities

How many words begin with R and end with Y?
Ans :
Begin = R , End = Y
Other 6 letters --> 26^6 ways

How many words start with A or B?
Ans :
Begin with A --> 26^7 ways
Begin with B --> 26^7 ways

Begin eith A or B = 2*26^7 words

How many words begin with A or end with B?
Ans :
Begin with A --> 26^7
End with B --> 26^7
Begin with A and end with B --> 26^6
So, 26^7 + 26^7 - 26^6
2(26)^7 - 26^6 words