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Lecture 5

6.4 notes permutations vs combinations.doc


Department
Mathematics
Course Code
MATH 011
Professor
Jarchow
Lecture
5

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Section 6.4: Combinations vs. Permutations
Permutation of n objects not all of which are distinct
Previously, we had n objects all of which are different
In this case, you divid out all repetitions in set
n!/ n(1)!, n(2)!....
Combinations: number of ways of selecting r objects from n objects
order is not important
C(n,r) = n!/ r! (n-r)! VS. P(n,r) = n!/ (n-r)!
Permutations Combinations
- numbers - groups
- words - committees
- schedule
-arrangement
-contest
-codes
ex: select 3 phones from 100 = combination
ex: 4 mutual funds from 8 can be grouped how many ways?
C(8,4)
ex: 6 candidates can be arranged how many ways on a ballot?
P(6,6) OR 6!
“or” = + = union
“and” = X = intersection
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