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10.3 Combinations

10.3 Combinations. Don’t forget about FCP, n!, and Permutations. Review . 1. What is the probability of getting three heads and a tail, when a 2-sided coin is tossed 4 times? 2. If a family of 6 is lined up to take a family picture, how many different ways can they line up?

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10.3 Combinations

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  1. 10.3 Combinations Don’t forget about FCP, n!, and Permutations

  2. Review • 1. What is the probability of getting three heads and a tail, when a 2-sided coin is tossed 4 times? • 2. If a family of 6 is lined up to take a family picture, how many different ways can they line up? • 3. If 6 track members run the 100 meter dash, how many ways can they place 1st, 2nd and 3rd? P(3 heads and a tail) =4/24 = 4/16= 1/4 6!=720 6x5x4 or 6P3= 6!/3! = 120 ways

  3. Combinations vs Permutations • How many different batting orders are possible on a team of 22 if 9 players bat? 22P9 Five players can take the court in basketball, how many possible ways could a coach select from 15 players to take the court? 15C5 The main difference between whether your dealing with a permutation or combination is whether or not ORDER matters.

  4. In the baseball example: • 22P9 = 22! We divide out the players 13! that do not bat. • In the basketball example: • 15C5= 15! Why the extra factorial? • 10!5! • Because not only do we have to divide out those not starting, we also divide out that it does not matter the order the 5 starters were chosen in?

  5. Combination Formula

  6. You try! No Calculator yet though

  7. Using the T.I. for P and C • You will also have to know how to do factorials, permutations and combinations without using the Math and prb key. • To do 8C3: Press 8, Math, go over to prb, press 3, then 3 ent

  8. Combo Practice • American Idol has 10 finalists, in how many ways can 2 be chosen to appear in the final show?

  9. Card Practice • 52 cards in a deck of cards • 26 red and 26 black • 13 each of four suits • hearts, diamonds, spades and clubs • 4 of each card • How many 5 card hands are possible? • How many 5 card hands are possible with all red cards?

  10. P(A) = # of possible outcomes # of total outcomes • What is the probability of getting a 5 card hand with all red cards? Lets try more on the board

  11. Combo Combinations • An intramural basketball team has 5 starters. On the team there are 6 boys and 4 girls. If the team must play 3 boys and 2 girls at all times, how many starting line-ups are there? Lets use a T.I. for this. 120 different starting line-ups

  12. Hmwk.Thursday with workday Friday • P.694(2,5-8,13-18,38-40,48-50) • P.697 Quiz (1-4)

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