Unit 3 Section 6 Permutations and Combinations.notebook
Permutations and Combinations
Unit 3
Section 16
January 05, 2015
Unit 3 Section 6 Permutations and Combinations.notebook
January 05, 2015
Factorial: the product of all counting numbers beginning with n and
counting backward to 1. (n!)
...
Example: 4! = 4 3 2 1 = 24
1) Find the value of 5!
2) Find the value of 7!
Unit 3 Section 6 Permutations and Combinations.notebook
January 05, 2015
Permutations and Combinations
What's the Difference?
In English we use the word "combination" loosely, without
thinking if the order of things is important. In other words:
"My fruit bowl is a combination of apples, grapes and bananas" We don't
care what order the fruits are in, they could also be "bananas, grapes and
apples" or "grapes, apples and bananas", its the same fruit bowl.
"The combination to the safe was 472". Now we do care about the order.
"724" would not work, nor would "247". It has to be exactly 4-7-2.
If the order does matter it is a Permutation.
If the order doesn't matter, it is a Combination.
So, we should really call this a "Permutation Lock"!
Unit 3 Section 6 Permutations and Combinations.notebook
Permutations and Combinations
Permutation: an arrangement or listing in which order is important.
P(n,r) = n number of choices, taken r at a time
.
Example: P(5,2) = 5 4 = 20
3) How many ways can six swimmers be arranged on a four-person relay
team?
4) How many four-digit numbers can be made from the digits 1,3,5, and 7?
5) How many ways can 12 actors fill 5 roles in a play?
6) There are 20 dancers competing in a championship competition. How
many ways can the top 3 winners finish?
Combination: an arrangement or listing in which order is not important.
C(n,r) = P(n,r)
r!
..
Example: C(6,2) = P(6,2) = 6 5 = 15
2! 2 1
7) How many ways can students choose two school colors from red, blue,
white and gold?
8) How many ways can three flowers be chosen from tulips, daffodils,
lilies, and roses?
9) Find the number of line segments that can be drawn between any two
vertices of an octagon.
10) How many ways can 2 pairs of shoes be chosen from 12 pairs?
11) How many ways can a 9 person baseball team be chosen from a group
of 18 students?
January 05, 2015