They're taking the multiset [0].
So it's \binom{2^4 + 4 - 1}{4} = 3876
In other words, there are 3876 multisets of cardinality 4 with elements taken from the set containing all 4 bit values.
So it's \binom{2^4 + 4 - 1}{4} = 3876
In other words, there are 3876 multisets of cardinality 4 with elements taken from the set containing all 4 bit values.