Question

Consider the finite strings of length 100 drawn from the alphabet of 4 letters {a,b,c,d}. How many of those strings use no more than two different letters?

Answer 1

`2^(100) * 6`

Explanation:

length of finite strings = 100

number of letters : 4 { a,b,c,d }

Determine the number of strings that use ≤ two different letters

since the number of letters is 4 and we are allowed to make use of at most 2 different letters

Then the number of ways will be :
`^(4) C_(2)` = 6 ways

now considering the length of the Finite strings

The number of strings that use no more than two different letters

=
`2^(100) * 6 ways`