# Math Help - How many bit strings of length 27 are there...?

1. ## How many bit strings of length 27 are there...?

How many bit strings of length 27 are there such that:

a. the bit string corresponding to the last twelve positions contain exactly seven 0

b. the bit string has at least fifteen 0 and at least ten 1, also must have the bit string corresponding to the first nine positions contains six 1and the bit string corresponding to the last twelve positions contain a maximum of ten 0.

c. the bit string corresponding to the first ten positions contain exactly eight 1 and a bit string corresponding to the last fifteen positions contains (or does not contain) the string as a sub-string 1011101

2. Hi,

I will attempt a.

For the last 12 positions there are $\binom{12}{7}$ ways to pick the 0's, once the 0's are fixed, the 1's fall naturally into position.

Then for the first 15 positions there are 2 choices for each positions, either a 1 or 0, thus there are $2^{15}$ choices for the 1st 15 positions.

Thus in total we have $\left(2^{15}\right)\binom{12}{7}$ bit strings.

I would really like to know if this is correct though, could someone confirm? Thanks.