A Pinochle deck is a special deck of cards with 48 cards in total. it consists of two copies of each of the 9, 10, J, Q, K and Ace of all four suits (so there are 2 nine of clubs, 2 nine of diamonds, 2 nine of hearts, two nine of spades, and so on for ever other denomination). Poker can be played with the Pinochle deck, but the probabilities are different from poker with a standard deck. Calculate the following from the Pinochle deck:
a) Total number of 5-card Poker hands possible (order does not matter)
Attempt: 48C5 = 1712304 (I believe this number includes repetitions, how do I get rid of those?)
b) Probability of a four of a kind (4 cards of the same denomination plus one card of a different denomination)
For this one, I know how to do it with a standard deck, as following, but not the Pinochle one. How would the numbers be changed? I know the technique is the same, but which numbers would end up changing?
Attempt: P(4 of a kind):_
Denominations: 13 C 1 x 12 C 1
Suits: 4C4 x 4C1
Total: 13C1 x 12C1 x 4C4 x 4C1 = 624
P(4 of a kind 52 cards) = 624/52C5 = 1/4165
So would the Pinochle probability be = 624/48C5 ?
c) Probability of a royal flush (A,K,J,Q, 10 all of the same suit)
Attempt: P(Royal Flush) = 8/(48 C 5) = 1/214038