Can you shuffle an album in the numerical order it appears on in the original track listing? Like, let’s say the album has 14 songs, statistically, if you shuffle enough times then the order of the songs would appear in the track list order, no?

Question

Can you shuffle an album in the numerical order it appears on in the original track listing? Like, let’s say the album has 14 songs, statistically, if you shuffle enough times then the order of the songs would appear in the track list order, no?

In: 3

Answer 1

The number of different ways to order N-many items can be calculated using something called “N-factorial” which is written as “N!”.

For three songs, that is three-factorial 3! many ways, and the definition of factorial means that this equals 3!=3x2x1=6 ways to order the songs… so randomly shuffling to the correct order would occur 1/6 of the time (about 16.7% of the time).

For four songs, 4!=4x3x2x1=24 so shuffling into the correct order has a 1/24 chance of happening (4.2% chance).

For five songs, 5!=5x4x3x2x1=120… so 1/120 (0.8%).

…For 14 songs, that 14!=14x13x12x11x10x9x8x7x6x5x4x3x2x1=87,178,291,200 amounts to ~87-Billion… so 1/87178291200 is crazy small.

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As for “Why does the factorial math describe the number of ways to shuffle something?” you gotta think about it in reverse.

There’s only one place to put the first song. 1

You can put the second song either before or after that. (1)x2

You can put the third song either before the other two, in between, or after. (1×2)x3

And so on!