Hi, I've been poring over these problems for a couple of days and I couldn't find the answer, so here I am. Thanks in advance!
1. A club has 33 men and 41 women members, including 14 male-female married couples. A slate of officers for this club consists of a president, secretary, and a treasurer. According to the club's rules, the secretary and treasurer cannot be of the same sex and cannot be married to each other. how many different slates of officers are possible if no person can hold 2 offices?
2. License plates shall consist of a sequence of 7 symbols, either letters different from "O," or digits 0-9. The plate must have at least one letter and at least one digit. How many cars can be registered using this scheme? Digits and letters can be repeated.