Kategorier
Gymnasiematematik(high school math) matematik 1c matematik 5 Probability Uncategorized

Combinations

It is called acombination of r elements if the order of the elements in a selection of r elements out of n elements is irrelevant and redundance is not allowed. Another way of ststing this is to say that all elements are selected at once and not one-by-one.

This number is given by the ratio n!/(n-r)!. It is also necessary to divide by r!  since redundance is not allowed.

Ex. The capital of Madagascar is called ANTANANARIVE.

The number of letters here is 12 but to find all permutations we need to take into consideration that we have three N therefore we get the same word independently of their internal order and must theefore divide by 3!. The same is the case for the four A which force us to divide by 4!.

The number of combinations for this word therefore is 12!/(4!3!).

Generally the number of subsets with r components selected out of n elements is

C(n,r) = n!/((n-r)!r!)