How many bit strings of length 10 begin with 1101SolutionWe

How many bit strings of length 10 begin with 1101?

We are dealing with strings of length 10. And we are asked to keep first 4 bit fixed as 1101

So, we are left with 10 - 4 = 6 bit which we can alternate to generate different combinations

each of 6 bit can be either 0 or 1

So each of 6 bit can be written in 2 ways

i.e total number of combinations possible is 2^6 = 64

So, there are 64 number of strings of length 10 begin with 1101 can be generated.