Hello,

Well, keep 000 at the beginning.

Then there are 7 remaining bits that are to be chosen.

Each with two possible values : 0 & 1.

So it's 2^7.

Now, keep 1111 in the end.

There are 6 remaining bits that are to be chosen.

Each with two possible values : 0 & 1.

So it's 2^6.

Total number : 2^7+2^6 (if you have to include the case where it both starts with 000 and ends with 1111)