I CAN: Use Permutations and Combinations
12
Chapter 1 Section 11-3 I CAN: Use Permutations and Combinations
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Guidelines on Which Method to Use Permutations Combinations Order matters! Order doesn’t matter! Arrangements of n items taken r at a time Subsets of n items taken r at a time Clue words: arrangement, schedule, order, rank, holding offices (Pres), rearranging numbers Clue words: group, sample, selection, committee
Transcript of I CAN: Use Permutations and Combinations
Chapter 1
Section 11-3I CAN: Use Permutations and
Combinations
Guidelines on Which Method to Use
Permutations CombinationsOrder matters! Order doesn’t matter!Arrangements of n items taken r at a time
Subsets of n items taken r at a time
Clue words: arrangement, schedule, order, rank, holding offices (Pres), rearranging numbers
Clue words: group, sample, selection, committee
1-3-3
Factorial Formula for Permutations
Arrangements are called permutations The number of permuations of n things taken r at a time is denoted as: ! .
( )!n rnP
n r
ORDER MATTERS
n = _________________r = _________________
n must be greater than r
*Can’t have more #s in a subset than the total # of items!
Example: Permutations
Evaluate each permutation.
a)5P3 b) 10P4
Example: IDs
How many ways can you select two letters followed by three digits for an ID if repeats are NOT allowed? TWO PARTS!!
…or how did we do this question in 11.2?
___ ___ ___ ___ ___
Example: Building Numbers From a Set of Digits
How many four-digit numbers can be written using the numbers from the set {1, 3, 5, 7, 9} if repetitions are not allowed?
Factorial Formula for Combinations
In counting problems, subsets where the order of the elements makes no difference are called Combinations:
! .! !( )!
n rn r
P nCr r n r
*ORDER DOES NOT MATTER*
The # of combinations of n things taken r at a time
Example: Combinations
Evaluate each combination.
a)5C3 b) 7C2
11-3-9
Example: Finding the Number of Subsets
Find the number of different subsets of size 3 in the set {m, a, t, h, r, o, c, k, s}.
Example: Finding the Number of Poker Hands
A common form of poker involves hands (sets) of five cards each, dealt from a deck consisting of 52 different cards. How many different 5-card hands are possible?
Repetitions are not allowed and order is not important.
Example: Forming Committees
A city council has 8 members. The council needs to set up a committee of 5 for a zoning issue. In how many ways can a committee be selected?
11.3 Book Work
p. 702 #1-15 odd, 19-27 odd (skipping 17), 37, 53
