In the Permutation section, we look at situations where the ordering makes a difference. Drawing an Ace first and then a Ten is assumed to be different than drawing a Ten first and then an Ace. In the casino, normally the order of cards making up a Blackjack do not matter. In other words, we generally get paid a 3 to 2 bonus regardless of the order in which the cards are dealt. So, when talking about combinations, keep in mind that the ordering does not matter.

Combinations of "n" Distinct Items:
Take any 5 cards, say Queen, Two, Six, Four, and Jack; this is one five-card combination. Notice that there are (5)(4)(3)(2)(1) ordered sequences. In other words, we count 120 permutations. Can you understand the difference between combinations and permuatations? We have one five-card combination, and with the same five cards we have 120 permutations.

In summary, the number of combinations of "n" distinct items is always 1.


Combinations of "r" Out of "n" Distinct Items:
Let's say we now have 20 cards, out of which we select 5. In general, the number of r-item combinations using "n" distinct items is:

n!/(r!(n-r)!)

Special Note: We define 0! = 1