Pascal's Triangle

Binomial coefficients are written C(r;c) and represent "the number of combinations of r things taken c at a time." The numbers in Pascal's Triangle are simply the binomial coefficients. The importance of binomial coefficients comes from a question that arises in every day life. An example is a how to take three books from a shelf two at a time. The first two books alone would be one way to take two books from a set of three. The other ways would be to take books two and three or books one and three. This gives three ways to take two books from a set of three. For larger arrangements, listing the number of combinations can be nearly impossible. So instead, the binomial coefficient can be found instead. For the above three books taken two at a time, all that needs to be found in the binomial coefficient C(3,2), which is the third row and second column of Pascal's triangle, or three.