In a standard deck of cards plus 1 additional joker (53 cards), I am trying to calculate the probability of drawing a Three of a Kind and a Joker in the same 5 card hand.
At the moment I know the probability for drawing a three of a kind is:
${^{13}\mathrm C_1}\times{^4\mathrm C_3}\times{^{12}\mathrm C_2}\times({^4\mathrm C_1})^2 ~/~ {^{53}\mathrm C_5}$
I am just wondering how I would add in the joker
(this is for school and any help would very appreciated)