A combination is term used in probability to indicate how many different subsets of a particular size can be formed from a larger set. Unlike a permutation the ordering of the elements of the set is not important. For example, in a 52 card deck there are 1326 different 2-card combinations.

The above is the number of combinations of cards in a standard 52 card poker deck. For contrast the number of permutations is also shown.

Ordering

In a combination the ordering of the elements is not considered. This is the same rule when forming poker hands: the order of the cards in your hand, or on the board, is not relevant. The two pockets A♦ 5♠ and 5♠ A♦ are equivalent.

This may cause particular confusion since in poker cards are dealt in a very specific order, with breaks in between to allow betting. How a person bets is heavily influence by the particular order in which they receive their cards. This however does not have any influence on the final valuation of their hand.

Calculation (Binomial Coefficient)

The formula to count combinations is called the binomial coefficient, otherwise known as the choose operator. The number of ways to select two cards of the same suit is 13 choose 2 -- in compact form (13c2).

The binomial coefficient is defined as (nCk) = n! / ( k! * (n-k)! ). Without using a specialized program however it cannot be precisely calculated this way as the numbers involved in poker far exceed the limits of a normal program. The results however do not.

Another way to think of combinations is as the number of permutations divided by the permutations of the positions. That is, (nCk) = (nPk) / k!. Understanding the calculation this way helps in some probability questions.