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# Combinations

 Glossary of Statistical Terms 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. Binomial coefficient, английскийCombinationsБиномиальный коэффициентThe binomial coefficient counts the number of ways n items can be partitioned into two groups, one of size k and the other of size n-k. it is computed as see also: binomial distribution, multinomial coefficient. Replacement, английскийЗаменаЗамещение; возмещение; воспроизводство^An operation to replace part of the body with an artificial partN подстановка replacive a замещающий, подстановочныйConstruction of a new pipe or underground utility located on or off the line of the existing systems, which serves the same function as the old system.Pronounced, английскийA заметный, явный (син. noticeable) accent Mutually exclusive, английскийDisjoint events or disjoint setsВзаимоисключающийBinomial coefficient, английскийCombinationsБиномиальный коэффициентThe binomial coefficient counts the number of ways n items can be partitioned into two groups, one of size k and the other of size n-k. it is computed as see also: binomial distribution, multinomial coefficient. 