The Mathematics of Shuffled Cards

It is said that each time you shuffle a 52-card deck,  each arrangement you make may have never existed in all history, or may never exist again. Why? Because of the enormous number of arrangements that can be made using 52 distinct objects (in this case, cards).

To understand this, we can look at the number of arrangements that can be made with smaller number of objects. Lets start with 3 objects A, B, and C. The possible arrangements are ABC, ACB, BAC, BCA, CAB and CBA. Notice that for the first position, there are 3 possible choices (see figure below). Then, after you made the first choice, there are only 2 possible choices left. And after the second choice, you only have 1 possible choice. This means that the number of arrangements of 3 objects is 3 \times 2 \times 1 = 6» Read more