Question

A group of 7 friends are playing poker one night, and one of the friends decides to try out a new game. They are using a standard 52-card deck. The dealer is going to deal the cards face up. There will be a round of betting after everyone gets one card. Another round of betting after each player gets a second card, etc. Once a total of 7 cards have been dealt to each player, the player with the best hand will win. However, if any player is dealt one of the designated cards, the dealer collects all cards, shuffles, and starts over.

The designated cards are: Queen of Spades, Ace of Hearts. The players wish to determine the likelihood of actually getting to play a hand without mucking the cards and starting over.

In how many ways can you deal the cards WITHOUT getting one of the designated cards?  (Hint: Consider how may cards are in the deck that are NOT one of the designated cards and consider how many cards need to be dealt in order for each player to have 7 cards.)

In how many ways can you deal each player 7 cards, regardless of whether the designated cards come out?

What is the probability of a successful hand that will go all the way till everyone gets 7 cards?     (Round your answer to 4 decimal places.)

Answer 1

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