Combinatorics

Question 1

nCk

Answer 1

n choose k

Find out how many different ways you can choose k items from n items set without repetition and without order.

This number is also called combination number or n choose k or binomial coefficient or simply combinations.

nCk = n! / (k! (n - k)!) for 0 <= k <= n

Question 2

nPk

Answer 2

In mathematics, the notion of permutation relates to the act of arranging all the members of a set into some sequence or order, or if the set is already ordered, rearranging (reordering) its elements, a process called permuting. These differ from combinations, which are selections of some members of a set where order is disregarded. For example, written as tuples, there are six permutations of the set {1,2,3}, namely: (1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2), and (3,2,1). These are all the possible orderings of this three element set. As another example, an anagram of a word, all of whose letters are different, is a permutation of its letters. In this example, the letters are already ordered in the original word and the anagram is a reordering of the letters. The study of permutations of finite sets is a topic in the field of combinatorics.

nPk = C(n,k) = n! / ( (n-k)! k!)