Transcript 10.3 – Using Permutations and Combinations Permutation: The number of ways in which a subset of objects can be selected from a.

10.3 – Using Permutations and Combinations
Permutation: The number of ways in which a subset of
objects can be selected from a given set of objects, where
order is important.
Given the set of three letters, {A, B, C}, how many possibilities are there
for selecting any two letters where order is important?
(AB, AC, BC, BA, CA, CB)
Combination: The number of ways in which a subset of
objects can be selected from a given set of objects, where
order is not important.
Given the set of three letters, {A, B, C}, how many possibilities are there
for selecting any two letters where order is not important?
(AB, AC, BC).
10.3 – Using Permutations and Combinations
Factorial Formula for Permutations
n!
.
n Pr 
(n  r )!
Factorial Formula for Combinations
n Pr
n!

.
n Cr 
r ! r !(n  r )!
10.3 – Using Permutations and Combinations
Evaluate each problem.
a) 5P3
b) 5C3
c) 6P6
d) 6C6
543
60
10
720
1
10.3 – Using Permutations and Combinations
How many ways can you select two letters followed by three
digits for an ID if repeats are not allowed?
Two parts:
1. Determine the set of two letters. 2. Determine the set of three digits.
26P2
10P3
2625
1098
650
720
650720
468,000
10.3 – Using Permutations and Combinations
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?
Hint: Repetitions are not allowed and order is not important.
52C5
2,598,960
5-card hands
10.3 – Using Permutations and Combinations
Find the number of different
subsets of size 3 in the set:
{m, a, t, h, r, o, c, k, s}.
9C3
Find the number of arrangements
of size 3 in the set:
{m, a, t, h, r, o, c, k, s}.
9P3
987
504
84
Different subsets
arrangements
10.3 – Using Permutations and Combinations
Guidelines on Which Method to Use