Hi, please help me with this counting/probability question. Thank you

4 Picking Teams (a) The 25 students in CS 70 have a strange way of picking a study group. Each person is given a distinct number 1 through 25 based on random chance, and participants may form a group as CS 70, Fall 2019, HW 7 2 long of the sum of their numbers is at most 162. (The TAs are afraid of the number 162 for some reason...) How many different study groups are possible? That is, how many different subsets of students are there, which are allowable under the ranking rule? (Hint: 162 = [(22:10 l] /2)) (b) UC Berkeley is forming a new, n-person robotics team. There are 2n interested students: It mechanical engineers and n programmers. (Assume that no student is both a mechanical engineer and a programmer.) Find the number of distinct n-person teams. (c) Suppose that all robotics teams must also name a team captain who is a mechanical engineer. Find the number of ways to pick an n-person team with a mechanical engineer as the captain