Problem 1. How many handshakes are possible given 6 people

Problem 2. A department has 12 faculty members. In how many ways can they elect a senator and an alternate senator?

Problem 3. How many 3 letter words (not necessarily in the dictionary) are there?

Problem 4. How many positive numbers < 1000 have their digits appear in order?

Problem 5. A department of 12 faculty needs to elect a committee of 4 including a chair. How many committees are possible?

Problem 6. Redo the 3 letter word problem using two sets: a set of 26 letters and a set of 3 positions. Check the two golden questions for your representation.

Problem 7. You want to elect a group of 4 out of 10. Try the representation {{?person:2}:2}, why is it wrong?

Problem 8. In how many ways can we seat 5 poeple on 3 chairs (not all get to sit of course)? Use two unordered sets, person and chair.

Problem 9. Repeat above by making one of the sets ordered, which one? One choice will lead to wrong representation (check the two Golden questions)

Problem 10. How many anagrams of "MATHEMATICS" are there? Use a set of 11 positions, and make each letter an identical set. Work with the Golden questions to check your representation.