1. Permutations and Combinations Independent Events: Events that do not affect each other Spinning a number 6 and then spinning a number 5 on the same spinner. Picking an ace out of a deck of cards and rolling a di and getting a 6 Picking an ace of hearts out of a deck of cards, then picking a jack of clubs out of the same deck with replacement. Dependent Event Events that affect each other. Picking an ace of hearts out of a deck of cards, then picking a jack of clubs out of the same deck without replacement.

2. Permutations and Combinations Basic Counting Principle: When one event can be chosen p ways and another event can be chosen q ways, then the events can have p*q ways Example: How many ways can Mr. Vogle make an ugly outfit if he has 5 pairs of ugly pants, 6 ugly shirts and 2 pairs of shoes? 5*6*2=60

3. Permutations and Combinations Permutations: P(n,n)=n! (permutation of n things taken n at a time) P(n,r)= n!/(n-r)! Order matters Example: How many ways can you arrange 5 subject books? P(5,5) =120

4. Permutations and Combinations Combinations:(order is not important)

5. Permutations and Combinations How many ways can you order 4 different class officers from a class council of 12 people? (Does order matter) P(12,4) How many ways can you order a 4 person sub committee from a class council of 12 people? C(12,4)

6. Permutations and Combinations At Kennedy High School there are 12 names on the ballot for sophomore class officers. Six will be selected to form a class committee. a.How many different committees of 6 can be formed? b.In how many ways can a committee of 6 be formed if each student has a different responsibility? c.If there are 7 girls and 5 boys on the ballot, how many committees of 3 girls and 3 boys can be formed? Answer to A A. Order is not important in this situation, so the selection is a combination of 12 people chosen 6 at a time. C(12, 6)=924

7. Permutations and Combinations At Kennedy High School there are 12 names on the ballot for sophomore class officers. Six will be selected to form a class committee. b.In how many ways can a committee of 6 be formed if each student has a different responsibility? Answer P(12, 6) =665,280

8. Permutations and Combinations At Kennedy High School there are 12 names on the ballot for sophomore class officers. Six will be selected to form a class committee. c.If there are 7 girls and 5 boys on the ballot, how many committees of 3 girls and 3 boys can be formed? Answer Since the events are independent, the answer is the product of the combinations C(5, 3) and C(7, 3). C(5, 3)  C(7, 3) =350