Background:

Write a Java method for the Spock problem c(n, k) seen in class. Include output code that shows the actual sequence of calls that are made and the value that they will return when the method is executed. For example, c(3,2) outputs the following: 1. c(3,2) c(2.1) + c(2,2) c(1,0) 1 c(2.2) 1 Name your method c. Example method specification: public static int c(int n, int k) Mr. Spock's Dilemma (Choosing k out of n Things) Problem Mission of Enterprise is to explorer new worlds Unexplored solar system that contains n planets Time will allow for visits to only k planets . How many different choices are possible for exploring k planets out of n planets in a solar system? Mr. Spock is especially fascinated by Planet X. . Order does not matter . Let .c(n, k) be the number of groups of k planets chosen from n In terms of Planet X: c(n, k) (the number of groups of k planets that include Planet X) (the number of groups of k planets that do not include Planet X) Base cases If time is available to visit all the planets (k- n) There is one group of everything c(k, k) 1 If no time is available to visit any planet (k-0) There is one group of nothing c(n, 0) 1 .If time is available to visit only one planet