The likelihoods of being dealt various poker hands are widely published (easily found on the internet). A more difficult problem is: what are the likelihoods of being dealt each poker hand, given a 54 card deck (52 card deck + 2 jokers).
The various hands of interest are:
3 of a kind
4 of a kind
5 of a kind
* Jokers can count as any rank card, in any suit.
(In reply to re(2): More results and solution
ugh, thank you. My problem lied in the fact that I counted the
combinations incorrectly and made an error in my straight flush
calculations that hid that from me. I am now in agreement from
the top down to straights, carrying on from there...