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Phill Black, a former Navy SEAL instructor has developed a game called the Push Up Game (PUG for short). The game consists of drawing a card from the FitDeck, a pack of 56 cards, and doing the exercise listed on the card (many are different variations on push-ups). He claims that the FitDeck cards can be shuffled to produce more than 3 trillion workouts. Assuming that all of the cards are unique, how many different workouts can be created by shuffling the deck and then doing the exercise on each card in the order they are drawn? Is his claim accurate? Explain why or why not?

 Feb 4, 2019
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ok So Phil is going to do one exercise from each of 56 cards. 

Each card has just one exercise.

The only thing differnt between the workouts is the ORDER that the exercises are done in.

so there is   

 

56! ways that the cards can be ordered.   

56! =

=710998587804863451854045647463724949736497978881168458687447040000000000000 = 7.1099858780486345e74

 

so

56!   is about    7.1 x  10^74    ways to order the cards.     That is way more than 3 trillion orders.

 Feb 4, 2019

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