permutations and combinations: Information from Answers.com

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.

For more information on permutations and combinations, visit Britannica.com.

	Algebra: In Simplest Terms - Permutations and Combinations (1991 Education Film)
	Ackerman-Proffit orthogonal analysis
	combinatorial analysis (mathematics)

	How do you tell the difference between permutations and combination questions in advanced maths? Read answer...
	Why are the answers from a permutation bigger than from a combination? Read answer...
	How many ways can 4 people be chosen from a group of 9and is this a combination or permutation? Read answer...

	Who invented permutation and combination formulae?
	What is the Difference between permutations and combinations?
	How we can recognised the combination and permutation easily?