A group of seven 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: 4 of Hearts, 7 of Spades, 5 of Diamonds. 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