A combinatorial coefficient is the whole number value for an expression in the form of _{n}C_{r}. For example, _{5}C_{3} represents the combinatorial coefficient 56. In real life, this would mean there are 56 ways to make combinations in groups three things out of a total of five different things (i.e. five ice cream flavors, three scoops per bowl). Combinatorial coefficients are also the coefficients in the expanded version of an expression in the form of (a+b)^{n}. So if your expression was (a+b)^{5}, the coefficients for each variable group (ex: a^{4}b) would be determined by the expressions _{5}C_{0, 5}C_{1, 5}C_{2, }and so on up until _{5}C_{5} (or _{n}C_{n}, in a more general sense). Combinatorial coefficients can also be called "binomial coefficients." |