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12.6 Permutation

12.6 Permutation. SWBAT apply permutations to solve counting problems. Permutation. An ordered arrangement of distinct objects without repetition Order matters!!!. Factorial. The product of all positive numbers less than or equal to the number. Problem 1.

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12.6 Permutation

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  1. 12.6 Permutation SWBAT apply permutations to solve counting problems

  2. Permutation • An ordered arrangement of distinct objects without repetition • Order matters!!!

  3. Factorial • The product of all positive numbers less than or equal to the number

  4. Problem 1 • How many permutations are possible for the letters A, B, C, and D?

  5. Problem 2 • In an American Kennel Club (AKC) sponsored field trial, the dogs compete in random order. If there are nine dogs competing in the trials, how many possible running orders are there?

  6. Problem 3 • Five contestants in the Miss America pageant reach the live television interview round. In how many possible orders can the contestants compete in the interview round?

  7. Permutations taken r at a time • nPr

  8. Problem 1 • The starters for a six-woman volleyball team have to be listed in a particular order (1-6). If there are 13 women on the team, how many possible starting lineups are there?

  9. Problem 2 • A softball team has 12 players, 10 of whom will be in the starting lineup (batters 1-10). How many possible starting lineups are there for this team?

  10. Permutations with repetition or a non-distinguishable permutation

  11. Problem 1 • The peg game on the tables at Cracker Barrel is a triangle with 15 holes drilled in it, in which pegs are placed. There are 5 red pegs, 5 white pegs, 3 blue pegs, and 2 yellow pegs. If all 15 pegs are in the holes, how many different ways can the pegs be aligned?

  12. Problem 2 • Suppose a similar game to the peg game at Cracker Barrel is set up with only ten holes in a triangle. With 5 red pegs, 2 white pegs, and 3 blue pegs. How many different permutations can fill that board?

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