Combinatorics continued

1
Combinatorics (continued)

• Permutations Review
• Combinations
• The Leftover Principle

2
Section 6.1 Exploratory Exercise 5
3
Permutations

• Permutations are used when creating arrangements
  for which ordering matters
• The number of r-permutations of a set of n
  objects can be determined using the formula

4
Combinations

• If we want to create arrangements for which
  ordering is not important, we use Combinations.
• The number of r-combinations of a set of n
  objects can be determined using the formula

5
Huh?

• (1) Lets consider taking r-permutations from a
  set of n-objects.
• (2) In how many different ways can we permute
  those r-objects?

(3) So if order doesnt matter we divide our
answer to (1) by our answer in part (2) to get
6
Other Notation

• Combinations of n objects taken r at a time can
  be denoted other ways as well

7
Compute The Following
8
The Leftover Principle

• You may have noticed that some of your answers
  were the same.
• The number of ways we could arrange 6 objects
  taken from a set of 9 would be the same as the
  number of ways we could arrange the 3 other
  objects that remain.

That's Amazing!
9
Pop Quiz!

• This quiz has 6 questions.
• You must select any 4 to answer.
• In how many ways can this be done?

10
Ride-share

• Eight colleagues living in the same neighborhood
  decide to carpool to work on a daily basis using
  a company car. The only problem is that the car
  only seats five. How many different groups of
  people can carpool together?
• ANSWER 56 combinations

11
Chinese Food

• At Emperors Gourmet Chinese Restaurant, dinner
  for eight consists of three items from column A,
  four items from column B, and three items from
  column C. If columns A, B, and C have five,
  seven, and six items respectively, how many
  different dinner combinations are possible?

12
6.2 Exercise Set 10a

• A package of jellybeans has 15 green jellybeans
  and 11 red jellybeans. In how many ways can you
  choose a handful of 5 jellybeans in which there
  are 2 green and 3 red jellybeans?

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6.2 Exercise Set 10b

• A package of jellybeans has 15 green jellybeans
  and 11 red jellybeans. In how many ways can you
  choose a handful of 5 jellybeans in which there
  are at least 3 red jellybeans?

STOP
14
Homework For Wednesday

• Section 6.1 20
• Section 6.2 6, 8