8.4 Permutations

8.4 Permutations
Factorial Notation
For any natural number n,
* 0! = 1
A set of n objects in an ordered arrangement of a certain number
of objects.
The number of permutations of a set of n objects taken k at a time is given by
Permutations on the Calculator
math ⇒PRB ⇒ nPr
Fundamental Principle of Counting
1.) An auto manufacturer produces 7 models, each available in 6
different colors, 4 different upholstery fabrics, and 5 interior
colors. How many different automobile varieties are available?
2.) A menu offers a choice of 3 salads, 8 main dishes, and 5
desserts. How many different 3-course meals are possible?
3.) A 5-digit zip code contains 5 numbers 0-9 which can be
repeated. How many different possible zip codes are there?
4.) How many different 4 letter arrangements can be written if
letters can be repeated?
How many ways can you arrange 8 people in a straight line?
Your mom gives you a list of chores that must be done: vacuum,
wash dishes, take out the trash, clean your room, walk to dog, dust,
and sweep the floors. She tells you that you must complete 4 of
the chores. How many different ways can you arrange the chores?
Permutations: More Examples
How many different ways can 9 baseball players be arranged on
the baseball field? If there are 15 people on the team, how many
ways can they be assigned to 9 positions?