Why is the binomial coefficient $\binom00$ equal to 1?

binomial-coefficients

How many subsets of size $4$ are of a set of size $7$?

$$7\choose{4}.$$

How many subsets of size $0$ (i.e., empty sets) are there in a set of size $0$?

$$0\choose 0$$

which is $1$, because the empty set has exactly $1$ subset of size zero, namely itself.

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