Question

How many ternary strings of length 8 begin with 01 or end with 1? (A ternary string consists of 0s, 1s, and 2s.)

Answer 1

We know length of string that is 8.

We want to start with 01 or end with 1

So let us consider the string which starts with 01 so we are left with 6 places to fill with 0s, 1s and 2s. There are 3 possibilities for each place hence total number of such string will be 3^{​​​​​​6}.

Now we want our string to end with 1. There are 7 places left to fill with 0s, 1s and 2s. So each place has 3 possiblities hence there are 3^{​​​​​​7} such strings.

Since we want either of the strings. We will add both and hence there are 3^{​​​​​​6} + 3^{​​​​​​7} = 4*3^{​​​​​​6} strings of length 8 which begin with 01 or end with 1.