- Election problem
- tree diagram
- fundamental counting principle
- ordered pair/ordered triple
- define permutation
- notation for permutations
- evaluating permutations
- multiplication property of factorials
- count-down property
- permutation formula
- Distinguishable permutations
- indistinguishable items
- distinguishable items
- formula for distinguishable permutations
12.1 Essential Ideas
Fundamental Counting Principle
If one task can be performed in m ways, and if, after that task is completed, a second task can be performed in n ways, then the total number of ways of ways for both tasks is found by multiplication: mn.
A permutation of r elements selected from a set of n elements is an ordered arrangement of those r elements selected without repetitions. The order of selection is important.
Number of distinguishable permutations: If n objects are partitioned so that there are n1 of one kind, n2 of another, andn 3 of still a third kind (so that n1 + n2 + n3 =n), then the number of ways that the n objects can be selected is n! divided by the product of (n1)!(n2)!(n3)!.
Factorial: n ! = n(n − 1)(n − 2)(n − 3) … (3)(2)(1).
Count-down formula: n ! = n(n − 1) !
Permutation formula: The number of ways of selecting r elements from a set with cardinality n in which the order of section is important is n !/(n – r ) !