A group of 5 friends are playing poker one night, and one of thefriends decides to try out a new game. They are using a standard52-card deck. The dealer is going to deal the cards face up. Therewill be a round of betting after everyone gets one card. Anotherround of betting after each player gets a second card, etc. Once atotal of 7 cards have been dealt to each player, the player withthe best hand will win. However, if any player is dealt one of thedesignated cards, the dealer collects all cards, shuffles, andstarts over.

The designated cards are: 9 of Spades, 10 of Hearts, 2 ofDiamonds, 7 of Clubs. The players wish to determine the likelihoodof actually getting to play a hand without mucking the cards andstarting over.

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

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

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

Recall, while using your calculator, that E10 means to move thedecimal place 10 places to the right.