1. Unit 10-2 Geometric Probability
Permutations and combinations

2. Vocabulary Permutation Combination Factorial Theoretical Probability
Empirical Probability
An arrangement of objects in which order is important.
An arrangement of objects in which order is not important.
The product of the integers less than or equal to a positive integer n, written as (n!)
Determining the probability that something will happen based on a sample space and using the fundamental counting principal.
A scientific “guess” based on results of a probability experiment or actual outcomes of an event.

3. Permutation
Chanise and Renee are members of the lacrosse team. If the 20 girls on the team are each assigned a jersey number from 1 – 20 at random, what is the probability that Chanise’s jersey will be 1 and Renee’s will be 2?
Number of possible outcomes
Number of desired outcomes
with chanise #1 and renee #2 (20 – 2 ) = 18
Calculate probability
P (chanise 1, renee 2) =
Expand the factorial =

4. Combination
For her birthday, Monica can invite of her 20 friends to join her at a theme park. If she chooses to invite friends randomly, what is the probability that her friends: Tessa, Guido, Brendan, Faith, Charlotte, and Rhianna are selected?
Since the order of the friends does not matter, the number of possible outcomes in the sample space is the number of combinations of 20 people taken 6 at a time is
Since there is only 1 favorable outcome where these specific friends are selected, the probability is

5. Permutation
A football teams 11 players huddle together before a play. What is the probability that the fullback stands to the right of the quarterback if the team huddles randomly?
Since there is no fixed reference point, this is a circular permutation. There are (11-1)! Or 10! Distinguishable permutations of the players. The number of favorable outcomes is the permutation of the other 9 players’ positions in the huddle, or 9!. So the probability that the fullback stands to the right of the quarterback is
If a referee stands directly behind the huddle, what is the probability that the referee stands directly behind the halfback?
Now there is a fixed point of reference. The number of favorable outcomes is the number of permutations of the other 10 players.

6. Permutation
Nina and Chad are going to a concert with their high school’s Key Club. If they choose a seat on the row below at random, what is the probability that Chad will be in seat 11 and Nina will be in seat 12? 6 7 8 9 10 11 12 13 14 15 16 17
Possible outcomes 12!
Desired outcomes (12 – 2 ) 10
P (chad 11, Nina 12) =

7. Permutation
A class is divided into teams each made up of 15 students. Each team is directed to select team members to be officers. If Sam, Valencia, and Deshane are on the same team, and the positions are decided at random, what is the probability that they are selected as president, vice-president, and secretary, respectively?
Order is important for this problem. The number of possible outcomes in the sample space is the number of permutations of the 15 people taken 3 at a time P3
15P3
Since there is only 1 favorable outcome for this situation

8. Calculating Probability
Students who score commended on their STAAR EOC for Algebra 1 are entered into a drawing for prizes. The top prizes are an Ipod touch and a Iphone 5C. If 12 girls and 8 boys are entered in the drawing, what is the probability the both top prize winners will be boys? What is the probability that the 2 top winners will include one boy and one girl?