The number of ways that m things can be 'chosen' from a set of n things is writen as:
and is interpreted as the number of m-element subsets (the m-combinations) of an n-element set, A.
It is called the choose function of n and m, and is defined to be the natural number:
Properties of binomial coefficient.
2. Recurrence relation:
4. Pascal's triangle
Let's see the first six rows of the Pascal's triangle:
Note that, in Pascal's triangle, the entries on the nth row are given by the binomial coefficients:
Pascal's triangle determines the coefficients which arise in binomial expansions.
Look that the coefficients in this expansion are precisely the numbers on row 5 of Pascal's triangle