1. Section 15.3 – Day 2 Counting

2. When do I use what? Rearranging things that are all different: Counting Principles (multiplication), Combinations, Permutations Choosing several things from a pool that contains all different things: Combinations, Permutations Rearranging things that have some of the same thing: Permutation with Repetition Choosing several things from a pool that contains some of the same things: Multiple Permutations/Combinations (multiply them!)

3. Gambler’s Lucky Bet You and your team are going to be playing the lottery. In each round you will have different lotteries to select from. In order to play the lottery you select, you must correctly show the probability for winning both lotteries.

4. Lucky Letters You must select letters from the following: AAABBC Lottery 1: Order the above letters into any arrangement your group desires. To win, your order must exactly match the winning order. You must select letters from the following: ABCD Lottery 2: Select two letters from the group above. To win, the house must pick the same two letters, order does not matter.

5. Lucky Letters You must select letters from the following: AAABBC Lottery 1: Order the above letters into any arrangement your group desires. To win, your order must exactly match the winning order and color. You must select letters from the following: ABCDEFG Lottery 2: Select two letters from the group above. To win, the house must pick the same two letters, order and color does not matter.

6. PowerPlay Number Swap Lottery 1: You must select 2 different numbers between 1 and 5. You win the jackpot if the same 2 numbers are drawn in any order. Lottery 2: You must select 3 different numbers between 1 and 9. You win the jackpot if the same 3 numbers are drawn in any order.

7. PowerPlay Number Swap Lottery 1: You must select 4 different numbers between 1 and 5. You win the jackpot if the same 4 numbers are drawn in the same order as you selected. Lottery 2: You must select 3 different numbers between 1 and 6. You win the jackpot if the same 3 numbers are drawn in the same order as you selected.

8. A Day At The Races The 132 nd running of the Kentucky Derby had a field of 20 horses. Bet 1: In horse racing, a trifecta is a bet that the first three finishers in a race are selected and they are selected in the correct order. You place this bet. Bet 2: In horse racing, a quinela is a bet that the first two finishers are selected, and they can be selected in any order. You place this bet.

9. Real Life PowerPlay Lottery 1: You must select 6 different numbers between 1 and 53. You win the jackpot if the same six numbers are drawn in any order. Lottery 2: You must select 6 different numbers between 1 and 53. You win the jackpot if the same six numbers are drawn in the same order as you selected.

10. Mini Quiz/Homework Quiz 1.) In how many ways can a club with 10 members choose a 3-person governing council? 2.) How many different ways are there to deal a hand of 5 cards from a standard deck of 52 cards if the order in which the cards are dealt is important? 3.) Many radio stations have 4-letter call sings beginning with K. How many such call signs are possible if letters can be repeated? 4.) Ohio State University has about 40,000 students. Explain why at least two students must have the same first, middle, and last initial.

11. Team Worksheet Practice Your homework tonight is to complete the following worksheet. Work with your team members to get as many problems done as you can.