Question

How many ways are there to deal 52 standard playing cards to four players (so that each player gets 13 cards)?

Suppose you are world champion in card dealing, and can deal 52 cards in just one second. Compare the time it would need you to deal all possible combinations with the current age of the universe. (If there are x ways of dealing the cards, then it takes x seconds for you to deal the cards. Now compare the age of the universe (use the same units) to x. )

Answer 1

Number of ways to deal 52 cards to 4 players = Number of ways of choosing 13 cards from 52 x Number of ways of choosing 13 cards from remaining 39 x Number of ways of choosing 13 cards from remaining 26 x Number of ways of choosing 13 cards from remaining 13

= 52C13 x 39C13 x 26C13 x 13C13

= 6.35x10¹¹ x 8.12x10⁹ x 10.4x10⁶ x 1

= 5.36x10²⁸

Time needed to deal all possible combinations = 5.36x10²⁸ seconds

= 1.70x10²¹ years

Age of universe is approximately 13.8x10⁹ years

So, the time needed to deal all combinations is 1.23x10¹¹ times more than the age of the universe