3.4.5 Multinomial Theorem Video
PROFESSOR: The binomial theorem extends to a thing called the multinomial theorem, whereas instead of taking a product of a sum of two things, you'd take the product of a sum of k things to get the multinomial theorem. And what underlies it is a rule that we're going to call the bookkeeper rule, and here's why. So, the bookkeeper rule is about the question of, look at the word bookkeeper and ask how many different ways are there to scramble the letters in this word that actually are distinguishable? The point being that the two o's are indistinguishable, so the order in which they appear doesn't matter. Likewise, the three e's and the two k's. Well, how do we answer this question? The simple way to do it to begin with is to label all of the indistinguishable letters with subscripts to make them distinguishable. So, I'm going to put subscripts 1 and 2 on the o's, 1 and 2 on the k's, and 1, 2, and 3 on the e's. Now, all the 10 let...