Transcript Permutations

12.7 Counting Methods and Permutations notes.
You will find the problems on the first page and the
completed solution on the other page.
Please read, interpret, and attempt each problem.
And then check the solution.
Multiplication Counting Principle
Ex1) Dick and Jane’s rehearsal dinner has the following choices:
Appetizers: soup, salad
Entrees: chicken, beef, fish, tofu
Desserts: apple pie, cheese cake
Multiplication Counting Principle
If there are p ways to make a first selection, q ways to make
a second, r ways to make a third, and so on, there are
p q r  ...
ways to make the selections.
Ex2) Suppose you have 3 shirts, 4 ties, and 2 pants that all
coordinate. How many possible outfits are there?

Permutations
A permutation is an arrangement of objects in a specific order.
Ex3) How many ways can 8 swimmers be assigned in 8 lanes?
Ex4) From a class of 25 students, how many ways can 4 students
exit the classroom?
Ex5) How many 4-number garage door combinations are possible?
Permutations
A permutation is an arrangement of objects in a specific order.
Ex3) How many ways can 8 swimmers be assigned in 8 lanes?
Ex4) From a class of 25 students, how many ways can 4 students
exit the classroom?
Ex5) How many 4-number garage door combinations are possible?
Permutations
Ex6) How many license plates are possible with 2 letters and 3
numbers if no numbers can be repeated?
Ex7) How many 4-number codes are possible if the first number
can’t be zero and no numbers can be repeated?
Ex8) SKIP
Permutations
Ex6) How many license plates are possible with 2 letters and 3
numbers if no numbers can be repeated?
Ex7) How many 4-number codes are possible if the first number
can’t be zero and no numbers can be repeated?
Ex8) SKIP
Permutations
The expression nPr represents the number of permutations
of n different objects arranged r at a time.
n
Pr  n(n 1)(n  2)...
r factors
Ex9) Simplify the following permutations.

a) 7P3
c) 5P5
b) 25P4
d) 12P1
Permutations
The expression nPr represents the number of permutations
of n different objects arranged r at a time.
n
Pr  n(n 1)(n  2)...
r factors
Ex9) Simplify the following permutations.

a) 7P3
c) 5P5
b) 25P4
d) 12P1
Permutations
Ex10) Suppose you use five different letters to make a password.
Find the number of possible five-letter passwords.
Permutations
Ex10) Suppose you use five different letters to make a password.
Find the number of possible five-letter passwords.
12.7 – Counting
Methods and
Permutations
HW: p.702 #1-5,
7-15, 27