a)There are n distinct elements
Now, we have to find at least one element occurs exactly twice
For example, multiset could be {1,1,2,2} or {1,1,2,3}
As it is construction of a set arrangement not required.
For 1st one where both elements repeats , multiset could be $ \binom{n}{2}$
For 2nd one where only one element repeates, multiset could be $ \binom{n}{3}.\binom{3}{1}$
So, we will just permute when total number of multiset where " at least one element occurs exactly twice "$=^{n}\textrm{C}_{2}+3.^{n}\textrm{C}_{3}$
b)It will be infinite