Permutations and card Shuffle

Permutations enable us to calculate the number of ways of arranging something and when the order matters. An example is the number of unique manners of placing three people, A, B, and C, on a podium, where first, second and third matter!

A B C	A C B	B A C
B C A	C A B	C B A

The formula for the permutations of n available options taken r at a time is _nP_r.

$_nP_r = \frac{n!}{(n-r)!} = \frac{3!}{0!} = 3 * 2 * 1= 6 \text{; for 0! = 1} \\$

So, what is the number of unique ways of shuffling a deck of cards?

$_{52}P_{52} = \frac{52!}{(52-52)!} = \frac{52!}{0!} = 52! = 8.1 \text{x}10^{67}$

Eight followed by 67 zeroes is a mind-blowingly large number and is far more than the number of atoms on this planet. Next time, when you shuffle a deck of cards, remember this arrangement may never have happened in this history and may never be happening again.

Factorial Calculator

Number of atoms in the world: Fermilab

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