1. 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).

2. 10.3 – Using Permutations and Combinations
Factorial Formula for Permutations
Factorial Formula for Combinations

3. 10.3 – Using Permutations and Combinations
Evaluate each problem.
b) 5C3
c) 6P6
d) 6C6
a) 5P3
543 60 10
720 1

4. 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

5. 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

6. 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}.
Find the number of arrangements of size 3 in the set: {m, a, t, h, r, o, c, k, s}.
9C3
9P3
987
504
arrangements 84
Different subsets

7. 10.3 – Using Permutations and Combinations
Guidelines on Which Method to Use