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Combinations

Combinations. Section 12.6. Combinations. ORDER IS NOT IMPORTANT Picking members for football tournament Picking members for debate team. Combination Formula. Permutation Formula n P r : n! / (n-r )! Combination Formula: n P r : /r! n ! /r! (n-r)!

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Combinations

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  1. Combinations Section 12.6

  2. Combinations • ORDER IS NOT IMPORTANT • Picking members for football tournament • Picking members for debate team

  3. Combination Formula • Permutation Formula nPr : n! / (n-r)! • Combination Formula: nPr :/r! • n! /r! (n-r)! • What is happening by dividing by r! • How many ways can I arrange the numbers 1,2,3 • 3P3 3! • How many ways can I arrange the r object • rPrr! • Example 4C3= 4! / [(3)!(4-3)!] 4! / 3! 1! 4 • 8C5= 8! / 5! (8-5)! 8! / 5! 3! 8*7*6*5! / 5! 3! • 9C3= 9! / (9-3)! • 11C8 • 9C9 • 11C2 • 11C0

  4. Checking • 9C2 • 7C3 • 6C6

  5. Comparing Permutation/combination • How many ways you can arrange play list on your phone. • How many groups of 4 vegetables you can choose from 8 vegetables to make a soup • How many ways to choose 2 co-captains from 10 players. • Choosing a debate team of 4 people from 10 people.

  6. Permutations with duplications • How many ways to arrange the letters in the word BANANA? • How many letters? • How many are being arranged? • 7P7 • Eliminate duplicate letter N by dividing by 2! • Eliminate duplicate letter A by dividing by 3! • Final Answer : 7P7 / (2! * 3!) • 7*6*5*4*3*2*1 / (2*1 * 3 * 2*1)

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