Binomial And Multinomial Theorem. N r represents 1. The number of ways to select r objects out of n given objects unordered samples without replacement.
If x1 x2 are real numbers and nis a positive integer then. 3 6 the binomial and multinomial theorems we have previously learned that a binomial is an expression that contains 2 terms and a multinomial is any expression that contains more than 1 term so a binomial is actually a special case of a multinomial. The multinomial theorem provides a formula for expanding an expression such as x1 x2 xk n for integer values of n.
Proceed by induction on m.
Also as with the binomial theorem quantities of the form x 0 that appear are taken to equal 1 even when x equals zero. Proving the multinomial theorem by induction for a positive integer and a non negative integer when the result is true and when the result is the binomial theorem. This version is convenient for hand calculating binomial coefficients symmetry property. In statistics the corresponding multinomial series appears in the multinomial distribution which is a generalization of the binomial distribution.
