is the number of ways in
which k items can be chosen from amongst a set of n items.
The coefficients on the monomials in the expansion of a power of a binomial.
Combinatorially, these numbers have an interpretation as a "choice counter",
i.e. the binomial coefficient is the number of ways in
which k items can be chosen from amongst a set of n items.
![\[ \binom{n}{k} = \frac{n!}{k! (n-k)!} \]](B_2.gif)
The binomial coefficients form the rows of Pascal's triangle .
Let n be a positive integer. Then for all x and y,
![\[ (x+y)^n = \sum \binom{n}{k} x^k y^{n-k} \]](B_3.gif)
where the sum is taken from k=0 to k=n, and
is a binomial coefficient
.
A graph in which the set of vertices can be broken into two subsets such that there are no edges between vertices in the same subset. This concept extends naturally up to n-partite graphs.
A bridge in a connected graph is an edge whose removal would disconnect the graph. Edges which are bridges are also sometimes known as isthmuses. An easy example: in a tree, every edge is a bridge.
