72. In the expression $(1+x+y)^{20}$, the brackets are expanded, but similar terms are not combined. How many terms will be obtained in this case?
72. Let's expand the expression $(1+x+y)^{20}$, but we will not combine like terms. Each term that results from this is a product of twenty factors. Each of these factors is either 1, or $x$, or $y$. Therefore, our problem is equivalent to the following: in how many ways can 20 traffic lights be lit, each of which can shine either red, or yellow, or green?

Answer: $3^{20}$ (compare with problem 70).