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 math.r objects chosen from a set of math.n objects, expressed in factorial notation, is math.n! ÷ (math.n − math.r)! The number of combinations is math.n! ÷ [math.r!(math.n − math.r)!]. The (math.r + 1)st coefficient in the binomial expansion of (math.x + math.y)math.n coincides with the combination of math.n objects chosen math.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.
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The Australian and New Zealand punting glossary explains some of the terms, jargon and slang which are commonly used and heard on Australian and New Zealand racecourses, in TABs, on radio, and in the horse racing media. Some terms are peculiar to Australia, such as references to bookmakers, but most are used in both countries.
The emphasis in this list is on gambling terms, rather than the breeding or veterinary side of horse racing.