Hi fishguts! (innovative name by the way).

You seem to be going overboard on the numerator.

What exactly are you thinking of by multiplying your 3 aces by 13C1

and your 2 queens by 12C1 ?

Why do you feel that your numerator is not just 4C3 multiplied by 4C2,

which is "any pair of queens can be matched with any triple of aces"

?