# April 17th Problems

- How many ways can two dice (six-sided) be rolled to get a 9?
- How many ways can 4 dice by rolled to get a 6?
- Andy, Brahbrah/Barbara, and Chuck each roll two dice (Monopoly maybe?). How many ways can Andy roll a 10, Brahbrah roll a 7, and Chuck a 5?
- Suppose 13 men, 6 women, 2 boys, and 4 girls are the last survivors of the human race.
- How many ways can we film a 50s sitcom? That is, how many ways can they select 1 man, 1 woman, 1 boy, and 1 girl?
- How many ways can a man or a girl be selected? (This was the specified sacrifice (man or girl) for our new alien overlords.)
- How many ways can we select our new leader? (Select one human.)

- Let \(A = \{a_1, \ldots, a_n\}\) and \(B = \{1, 2, 3\}\).
- Prove that there are \(3^n\) functions from \(A \to B\).
- How many of these functions are
**NOT** onto?
- How many are onto?

- Calculate \(3^{80} \mod {7}\).
- Find the last 2 digits of \(7^{355}\).
- How many cards of a single suit must exist in a set of \(n\) cards drawn from a standard deck of playing cards? (A deck of cards has 52 cards divided into 4 suits of 13 cards each. I'm looking for the number of guaranteed cards for any one suit without specifying which suit.)
- How many ways can 10 adults and 5 children stand in a circle such that no two children are next to each other?