How many ways can you shuffle a deck of cards, so that the Ace of Hearts is not directly on top of the King of Hearts?
There are 52! ways to arrange the 52 cards of the deck
there are only 51 ways to have the ace of hearts directly on top of the king of hearts in the shuffled deck positions
but that leaves the other 50 cards to arrange in any order or 50!
52! - 51 * 50!= 52!-51! =
79107056417656496291436393839934463764226245720866291712000000000000 = 7.9107056417656496e67
( I think !)
Let us look at the number of ways in which the ace of hearts could be directly on the king of hearts
These two cards could occupy 51 positions.....and for each of these, the other cards could be arranged in 50! ways
The total number of arrangements= 52!
So....the number of ways that the ace of hearts is not directly on the king of hearts =
52! - 51 * 50! = 52! - 51! = EP's answer !!!!