Chapter 2 3 Counting Partitions Combinations Combination Combination
Chapter 2 -3 Counting Partitions: Combinations
Combination • Combination is just like permutation – you are counting the number of ways to pick from a set without repetition of elements • THE DIFFERENCE: Order does NOT matter! • For Instance: “ 123” is considered the same as “ 132” because it’s the same elements. – rearranging the elements does not change the fact that you are using a 1, 2, and 3 together.
Formula •
Example • You are ordering pizza from a local pizza parlor. There is a special on a 3 -topping pizza, so you decide to go with that. There are 8 toppings to choose from. How many different pizzas can be made?
Example 2 • How many ways can a committee of 3 be formed from 10 club members?
Permutation or Combination? 1. The number of ways to form a committee of president, VP, and treasurer from Permutation 10 students. 2. Number of ways to select 5 distinct roles for a play out of 10 potential actors. Permutation 3. Number of ways to pick a hand of 5 cards from a deck of cards. Combination 4. Number of ways to award 1 st, 2 nd, and 3 rd place prize among 8 contestants. 5. Picking a team of 3 people for a team out of a group of 10. Permutation 6. Joan has five panels at home she wants to paint. She has 5 different colored Combination paints and intends to paint each panel a different color. Permutation
• A joke: A "combination lock" should really be called a "permutation lock". The order you put the numbers in matters. (A true "combination lock" would accept both 10 -17 -23 and 23 -17 -10 as correct. )
Choosing From Multiple Pools • There are 4 Democrats and 3 Republicans forming a committee with 2 Democrats and 2 Republicans. How many different committees could be formed?
Multiple Scenarios • A group of 6 friends are thinking about a Spring Break trip to FLORIDAAAAA! At least 4 of them have to go in order to get the group flight discount. How many groups can be formed such that they can get the discount?
Golden Rule • “AND” you multiply, “OR” you add. • When we need 2 Democrats AND 2 Republicans, we multiplied. • When we need a group of 4 OR 5 OR 6, we added.
- Slides: 10