ABSTRACT
The binomial coefficient gives the number of different groups of r objects which may be selected from a collection of n objects: e.g. there are different pairs of letters which may be selected from the four letters A, B, C, D; they are (A, B), (A, C), (A, D), (B, C), (B, D) and (C, D). The order of selection is presumed immaterial, so (B, A) is regarded as the same as (A, B) etc. As a more substantial example, the number of different hands of five cards which may be dealt from a full pack of 52 cards is .
