Discrete Mathematics Problem 3 Weekend trip to Vegas. For each sub-problem, reduce your final answer to a single integer and show your work. i) A standard 52-card deck has four suits (Hearts, Diamonds, Clubs, and Spades) and each suit has 13 ranks (2,3,4,5,6,7,8,9,10,Jack,Queen,King,Ace). The face cards are Jack, Queen, and King. How many ways are there to be dealt any 2 cards from a 52-card deck? (We are counting as distinct the same two cards received in a different order.) ii) How many ways are there to be dealt Blackjack? To be dealt Blackjack, either the first card is an Ace and the second card is a face card or a 10, or the first card is a face card or a 10 and the second card is an Ace. (Again we are counting as distinct the same two cards received in a different order.) iii) How many ways can you be dealt two cards such that the first card is a spade and the second card is a face card?
Discrete Mathematics
Problem 3 Weekend trip to Vegas.
For each sub-problem, reduce your final answer to a single integer and show your work.
i) A standard 52-card deck has four suits (Hearts, Diamonds, Clubs, and Spades) and each suit has 13 ranks (2,3,4,5,6,7,8,9,10,Jack,Queen,King,Ace). The face cards are Jack, Queen, and King. How many ways are there to be dealt any 2 cards from a 52-card deck? (We are counting as distinct the same two cards received in a different order.)
ii) How many ways are there to be dealt Blackjack? To be dealt Blackjack, either the first card is an Ace and the second card is a face card or a 10, or the first card is a face card or a 10 and the second card is an Ace. (Again we are counting as distinct the same two cards received in a different order.)
iii) How many ways can you be dealt two cards such that the first card is a spade and the second card is a face card?
iv) How many ways can you pick three cards such that the first card is a spade, the second card is a one-eyed Jack, and the third card is a face card? (There are two one-eyed Jacks in a standard deck: the Jack of Hearts and the Jack of Spades. Hint: Break the problem down into 3 disjoint cases for the type of card received 1st, 2nd, and 3rd.
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