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Understanding Combinations and Permutations for Team Selection and Arrangements

This document explores the concepts of combinations and permutations, emphasizing their applications in various scenarios, such as forming football teams, debate groups, and arranging items. It covers the combination formula, which calculates the number of ways to choose items when order is not important, and the permutation formula for scenarios where order matters. Examples demonstrate calculations using these formulas, such as how to choose team members from a larger group and how to arrange letters in words considering duplicates.

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Understanding Combinations and Permutations for Team Selection and Arrangements

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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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