Number of ways a subset of objects can be selected from a given set of objects.
In a permutation, order is important; in a combination, it is not. Thus, there are six permutations of the letters A, B, C selected two at a time (AB, AC, BC, BA, CA, CB) yet only three combinations (AB, AC, BC). The number of permutations of r objects chosen from a set of n objects, expressed in factorial notation, is n ! ÷ (n -r)! The number of combinations is n ! ÷ [ r !(n -r)!]. The (r + 1)st coefficient in the binomial expansion of (x + y) n coincides with the combination of n objects chosen r at a time (see binomial theorem ). Probability theory evolved from the study of gambling, including figuring out combinations of playing cards or permutations of win-place-show possibilities in a horse race, and such counting methods played an important role in its development in the 17th century.