How many binary sequences of length 18 are there that start with a run of 1s - that is, a conseuctive sequence of (at least) one 1 - then a run of 0s, then a run of 1s, and then a run of 0s, such that one run of 1 has length of at least 8?
The answer given is: 2 X C(7 + 4 -1, 7) - 1 so if you could explain this answer in depth it would be greatly appreciated.