540 000 000 000 000 000 000 (540 quintillion, American, or 540 trillion, European) is the closest number to the number of possible permutations possible, However, it falls enormously short of the actual number. The number of ways one can arrange the 52 distinct playing cards in a straight line is massive.

To work out how many ways there are of arranging the standard 52-card deck is to multiply 52 by all the numbers that come before it, i.e. (52 x 51 x 50 ..… 3 x 2 x 1). This is referred to as “52 factorial” and is usually written as “52!” by mathematicians. The answer is so huge that it is easier to write it using scientific notation as “8.0658175e+67”, which means that it is a number beginning with 8, followed by 67 more digits.

It is precisely equal to:

80,065,817,517,094,387,857,166,063,685,640,376,697,528,950,544,088,327,782,400,000,000,000.

This is an extraordinary number which is greater than the estimated number of stars in the known universe or the estimated number of atoms on Earth.

To see how this is feasible, imagine 6 people wanting to sit down in 6 available chairs. The number of options is calculated by 6 x 5 x 4 x 3 x 2 x 1 = 720. Compare this with 4 people and 4 chairs where the number of options is 4 x 3 x 2 x 1 = 24. It is easy to see that when starting with the number 52, an enormously huge number of outcomes ensue.

It is important to shuffle the pack very well, at least 7 times, before playing cards.

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