Question

6. The game of FreeCell begins by dealing all of the cards from a standard deck into eight columns of cards. Four of these columns contain seven cards and four of these columns contain six cards. The order that the cards fall within a column matters, but the order of the columns does not matter. How many different deals are possible? Note: For this problem, you may report your answer as an expression rather than a final number. You can have 1 bonus point on homework if you are able to compute the number!

Answer 1

1st we choose a column of 7 cards among 52 cards are (52/7) ways since the order of cards within a column matter, so a column of 8 with any order can be chosen and since the columns does not matters we can choose 6 cards in a column and 7 cards in a column randomly, that does not affect the free cell dealing so the it od deals are 52!/45! Times 45!/38! Times 38!/31! Times 31!/24! Times 24!/18! Times 18!/12! Ties 12!/6! Times 6! = 52! = 8.65817517 times 10^67