Using the example of a soccer team again, find the number of ways to choose 2 strikers from a team of 11. As with permutations, the calculator provided only considers the case of combinations without replacement, and the case of combinations with replacement will not be discussed. Combinations, like permutations, are denoted in various ways including nC r, nC r, C (n,r), or C(n,r), or most commonly as simply ( NP r = n r CombinationsCombinations are related to permutations in that they are essentially permutations where all the redundancies are removed (as will be described below), since order in a combination is not important. The letters A through K will represent the 11 different members of the team:Ī B C D E F G H I J K 11 members A is chosen as captainī C D E F G H I J K 10 members B is chosen as keeperĪgain, the calculator provided does not calculate permutations with replacement, but for the curious, the equation is provided below: For example, in trying to determine the number of ways that a team captain and goal keeper of a soccer team can be picked from a team consisting of 11 members, the team captain and the goal keeper cannot be the same person, and once chosen, must be removed from the set.

In the case of permutations without replacement, all possible ways that elements in a set can be listed in a particular order are considered, but the number of choices reduces each time an element is chosen, rather than a case such as the 'combination' lock, where a value can occur multiple times, such as 3-3-3. Essentially this can be referred to as r-permutations of n or partial permutations, denoted as nP r, nP r, P (n,r), or P(n,r) among others. The calculator provided computes one of the most typical concepts of permutations where arrangements of a fixed number of elements r, are taken from a given set n.

11 permute 3