Possible Duplicate:
Counting subsets containing three consecutive elements (previously Summation over large values of nCr)
Suppose we have large number of two types of objects $A$ and $B$. Now lets say we have $N$ boxes. So if we try to arrange these two objects ($A$'s and $B$'s) in these $N$ boxes, we can arrange in $2^N$ possible ways. I want to count the number of arrangements in which there are at least $m$ contiguous $A$'s.
My approach was:
Lets combine those $m$ contiguous boxes containing $A$'s into 1 box. Now we are left with $n-m+1$ box. These boxes can be arranged in $(n-m+1)*2^{(n-m)}$ possible ways. But later I realized that it contains lots of repetitions (arrangements which are not unique). How can I remove these repetitions?? Or am I following a wrong approach entirely??