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May 21, 2022 at 13:41 comment added Ilya Bogdanov @MaxAlekseyev $k-1\choose \ell/2$ is the number of all strings where the first $1$ is to the right of the (\ell-k)$ th position. Among the subsequent ones, we search the next $1$ according to the same principle.
May 21, 2022 at 10:39 comment added Max Alekseyev Why $k$ changed into $k-1$?
May 20, 2022 at 6:05 history answered Ilya Bogdanov CC BY-SA 4.0