l3] [4] l3] 4- We want to distribute 101 cookies to three children: Adam, Beata, and Colin. 0 Adam always eats two cookies at the same time. so we want to give him an even number of cookies, but not more than 20. 0 Beata has a birthday today, so we want to give her at least 20 cookies. 0 Colin can get any number of cookies. Find out how many ways we have to distribute the cookies. (a) Express the answer as a coefficient of some power of a: in an appropriate generating function f($) (Don't forget to explain why your formula is correct.) a polynomial (17w)a ' (b) Express f(.'1:} as (c) Use the binomial theorem to get the final