Math Lesson #10: How many ways to re-order 3 cards?

How many ways to order 3 cards? Well, we can chose the ace first... that leaves us two choices for the second card, the 4 or the 9:

So, we have either "Ace, 4, 9" or "Ace, 9, 4":

Or, we can choose to start with the 9, which again leaves us with two choices for the second card:

So, we have either "9, 4, Ace" or "9, Ace, 4":

Finally, we can chose to start with the 4, which leaves two choices for the next card, the 9 or the Ace:

So, we have either "4, Ace, 9" or "4, 9, Ace":

Taken together, we have 3 choices for the first card, leaving 2 choices for the second card, leaving just one choice for the third...

This is 3 x 2 x 1 = 3! = 6 ways of re-ordering the 3 cards. For 5 cards it would be 5! (factorial) = 120 possible shuffles.