General
What is a factorial?
It is the multiplication of all the descending counting numbers from a given positive integer.
P(4,2)
12
P(6,4)
360
Use the fundamental counting principle to solve for the amount of ways we can rearrange the word "WATER"
(To be done on the board)
120
How many different ways can a group of 4 girls be seated into 4 chairs?
24
What is a permutation?
It is all the different possible outcomes for a given scenario.
P(5,4)
120
P(8,6)
20,160
Use the fundamental counting principle to solve the amount of ways we can rearrange the letters in the word "DEATHS"
(To be done on the board)
720
Six teams are competing in a tournament. First place and second place get gold and silver medals respectively. How many groups of medal winners are possible if the order of teams matter?
30
What is the fundamental counting principle?
It is a method of solving for permutations.
# of Permutations = (choices for first event)(choices for second event)...
P(6,6)
720
P(8,8)
40,320
How many ways can 4 different people line up for a photo?
24
If a thief tries to unlock a combination lock with 5 digits, how many different combinations are possible if the last digit is a given 8?
(The combination lock is a number one with numbers 0-9)
3024
What are some real world examples of Permutations?
Gambling, the lottery, license plates, seating arrangements, etc.
P(7,5)
2520
P(9,7)
181,440
How many different 2 digit numbers can be made using only the numbers "1, 2, 3, 4".
12
How many ways can three a group of 12 boys can be seated on six chairs?
665,280
What does 'r' stand for in the permutation formula?
It is the number of "seats" to arrange the objects into.
P(7,7)
5040
P(12,9)
79,833,600
If you have 8 different flavors of ice cream, how many different combinations of 3 flavors can you choose, considering the order in which you choose them?
336
Five people are seated at a circular dinner table at a political function. How many ways can they sit if the president and secretary always have to be seated next to one another?
12 ways