categories of two pairs

I calculated earlier that there are 1584 threes-up hands:

n(threes up hands) = 1584
n(fours up hands) = 1584 * 2 = 3168
n(fives up hands) = 1584 * 3 = 4752
n(sixes up hands) = 6336
n(sevens up hands) = 7920
n(eights up hands) = 9504
n(nines up hands) = 11088
n(tens up hands) = 12672
n(jacks up hands) = 14256
n(queens up hands) = 15840
n(kings up hands) = 17424
n(aces up hands) = 19008