Combinations I
1. Find the number of possible different handshakes among 20 people.
2. Abdul, Ibrahim, and Hamed are on the the school basketball team, along with 10 others. A game starts with 5 players. How many starting rosters include at least one of the three named students, ignoring the positions each player plays?
3. A particular pizza deal allows the customer to choose 2 meat and 3 veggies for toppings. The store offers 6 meat and 10 veggies options. How many differently topped pizzas are possible under this deal, assuming the customer chooses the maximum number of toppings?
4. A particular pizza deal allows the customer to choose 2 meat and 3 veggies for toppings. The store offers 6 meat and 10 veggies options. How many differently topped pizzas are possible under this deal, assuming the customer can choose any number of toppings from no toppings up to the maximum?
Hint 1
Take a look at Problem Decisions #2 prime factorization.
5. Five readers want to check out 15 books from a library. How many ways to check out the books if each reader checks out exactly 3 books?
6. A set of cards have 4 colors with each color labeled from 1 to 13 for a total of 52 cards. Two different players each randomly picks two cards without any replacement. It is a good result if one of the card is 13, and the other card is 4 or under. How many ways to pick cards so that exactly one player has a good result?
Hint 1
By using a Venn diagram or otherwise, write an expression for ways of exactly one of persons A or B has good, using the ways of i) at least A good ii) at least B good, and iii) both good.