12-5 Combinations.

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Presentation transcript:

12-5 Combinations

Recall Permutations If we have 8 books, how many ways can we arrange 3 on a bookshelf? Two methods: OR 8 ∙ 7 ∙ 6 = 336

New Problem We have 8 books and want to take 3 on vacation with us, how many ways can we do it? Difference between these problems? ORDER doesn’t matter 1st prob: arranging on bookshelf 2nd prob: just tossing 3 books in suitcase

Combinations Formula Formula: “n Choose r” Memorize!! You will have to write out!!

From the previous example Order doesn’t matter, so it’s called a Combination! (8 books choosing 3)

Example 1 I have 12 people on ASB, choose 2 to be on a committee ORDER doesn’t matter! (They don’t have titles)

The Difference? (you don’t need to write every word!) I have 12 people on ASB, want to choose 2, 1 for Pres and 1 for VP It’s a different arrangement  Permutation! ORDER matters! You can solve using blanks OR 12 11=132

13 students try out for soccer team, choose 5 for team Example 2 13 students try out for soccer team, choose 5 for team Permutation or Combination? No mention of positions or titles Combination! or put in calc

Ex. 3—Word “Combos” How many combinations can be formed from the letters in the word NUMBER, taking them: 5 at a time? =6 b) 2 at a time? = 15

Ex. 4—Co-ed Teams In how many ways can a team be formed having 5 players be chosen from 6 girls and 4 boys: If all are eligible? 10 people total: = 252 b) If the team must have 3 girls and 2 boys? 6 girls choose 3, AND 4 boys choose 2 (Multiply!) = 120

Ex. 5—Probability with C The Debate team, 4 boys and 8 girls, travel to an out of state match. Their coach can fit 7 in her car. If they get in cars at random, what’s the probability the coach’s car has: a) 2 boys and 5 girls? b) All girls?

Ex. 5 Cont. Peter, Manual, 5 left The Debate team, 4 boys and 8 girls, travel to an out of state match. Their coach can fit 7 in her car. If they get in cars at random, what’s the probability the coach’s car has: c) All boys? d) Peter and Manual (2 of the boys)? Peter, Manual, 5 left

Homework Pg. 657-660 Q1-10, #1-13* EOO, 17-31 odd *1-13—Do Without a calculator first!! Write it out, then plug in calculator! See example below: