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Permutations and Combinations

Permutations and Combinations. Learning Objective: to determine the number of combinations are possible when order does or doesn’t matter. Warm-up (IN) a. How many 5 letter code words are possible from the first 7 letters of the alphabet if no letter is repeated? b. If letters are repeated?

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Permutations and Combinations

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  1. Permutations and Combinations Learning Objective: to determine the number of combinations are possible when order does or doesn’t matter • Warm-up (IN) • a. How many 5 letter code words are possible from the first 7 letters of the alphabet if no letter is repeated? • b. If letters are repeated? • c. If adjacent letters must be different? • 2. How many different pizzas can you order if there are 2 types of crust, 8 toppings, 3 sauces and 2 cheeses to choose from?

  2. Notes! POM - Permutation Order Matters! Permutation - an arrangement of objects in a specific order without repetition Ex 1 – How many ways can you arrange 5 books on a shelf 1 5 2 4 3 = 120 Shortcut! Factorial = ! on the calculator: Math, cursor to PRB = or A permutation of n objects taken r at a time... = or

  3. Ex 2 - 5 books but only putting 3 on the shelf = 60 = = Ex 3 - How many permutations of {A,B,C,D} if 2 at a time? 12 = Ex 4 - How many permutations of 10 objects taken 4 at a time? 5040 =

  4. Combination - a set of n objects taken r at a time without repetition - fewer than the number of permutations because the arrangement does not matter! i.e. AB = BA video = or Ex 5 - How many 4-person committees can be formed from a group of 10 people? Does order matter? Y or N Perm or Comb? 210 = = =

  5. Ex 6 – a. If 8 people want to hold office in an organization, how many ways to choose pres, vp, sec, and treas? Does order matter? Y or N 1680 = Perm or Comb? b. How many ways to get a committee of 3? Does order matter? Y or N 56 = Perm or Comb? **To determine whether you need to find permutations or combinations, see if rearranging the objects produces a different result!

  6. Out – How many different ice cream cones can I get if there are 31 flavors and I want 3 scoops? Summary – The difference between permutations and combinations is… Don’t forget about POW!! HW –

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