combination

The number of combinations of n things taken k at a time is the number of ways of picking a subset of k of the n things, without replacement, and without regard to the order in which the elements of the subset are picked. The number of such combinations is nCk = n!/(k!(n−k)!), where k! (pronounced "k factorial") is k×(k−1)×(k−2)× … × 1. The numbers nCk are also called the Binomial coefficients. From a set that has n elements one can form a total of 2n subsets of all sizes. For example, from the set {a, b, c}, which has 3 elements, one can form the 23 = 8 subsets {}, {a}, {b}, {c}, {a,b}, {a,c}, {b,c}, {a,b,c}. Because the number of subsets with k elements one can form from a set with n elements is nCk, and the total number of subsets of a set is the sum of the numbers of possible subsets of each size, it follows that nC0+nC1+nC2+ … +nCn = 2n. The calculator has a button (nCm) that lets you compute the number of combinations of m things chosen from a set of n things. To use the button, first type the value of n, then push the nCm button, then type the value of m, then press the "=" button.

Authorization Path: 2.5.6.4.38.0