Good day, I was playing Munchkin: Loot Letter (A "spinoff" of the card game Love Letter) with a friend of mine. There are 16 cards in the deck, and in 2 player games, you burn 3 cards face up. My friend managed to burn 2 unique cards and 1 card that had a duplicate card in the deck.
Let's say that the cards are A, B, and C where A and B are unique and Card C has 2 copies in the deck. The order does not matter as well.
I was thinking of the probability of this happening (burning 2 unique cards and 1 card that had a duplicate). At first, I was thinking along the lines of:
My general idea was that the chance of drawing 1st card was 1 out of the deck count, and the chance of drawing the 2nd card was 1 out of the deck count - 1, and the chance of drawing the 3rd card was 1 out of the deck count - 2 -- then those probabilities are multiplied.
However, this would only work assuming that all 16 cards are unique. However, one of the cards drawn/burned have 2 copies in the deck. Now I'm not sure how to take into account the probability of drawing a card that had 2 copies in the deck.
How does one proceed with calculating probability for this situation? I'm not sure how to proceed with this problem. Any help is very much appreciated. Thank you.