For example:
If n = 8 and m = 0: ans = 1
If n = 8 and m = 1: ans = 8
If n = 8 and m = 2: ans = ?
If n =256 and m = 3: ans = ?
2026-02-23 05:10:53.1771823453
How many strings of n bits are there which differ by exactly m bits?
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Just choose the $m$ bits out of $n$ to be different, so $n \choose m$