The answer to this question is $10 \choose 6$. However, I find this odd. Why would it be a combination in this case and not a permutation?
Ordering does not matter in combinations from my understanding, this would mean that $001 = 010$, which seems counterintuitive.
I do not understand why I have to use combinations for this problem.
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To clarify the issue, when I have two people {Bob, Alice}. I can only make 1 combination, since {Bob, Alice} and {Alice, Bob} are the same. However in a bitstring of two, I can have 01 and 10, wich are not the same.
Best Answer
A bit string of length 10 with 6 zeros can be described by a list of the 6 "places" where the zeroes sit. This involves choosing 6 numbers from the 10 possible places, hence 10 choose 6.