1. Of 35 students in my class, 11 do karate, 11 play piano, and 20 do tennis. 4 students play piano and do tennis, 3 students do karate and play piano, 5 students do tennis and practice karate, and 3 student do none of these. How many students do all 3?
2. Layla's club has 10 memebers. She needs to appoint a president, a vice- president, and a secretary. How many ways can she do this if:
a) each member can hold at most one office?
b) members can hold any number of offices?