binomial coefficient
, where n is a positive integer and r is an integer such that 0 ≤ r ≤ n, defined by the formula
Since, by convention, 0! = 1, we have 
These numbers are called binomial coefficients because they occur as coefficients in the Binomial Theorem. They are sometimes denoted by nCr; this notation arose as the binomial coefficient equals the number of ways of selecting r objects out of n (see selection). The numbers have the following properties:
It is instructive to see the binomial coefficients laid out in the form of Pascal's triangle.
- Euclidean construction
- Euclidean distance
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