Permutations and Combinations

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Presentation transcript:

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?

POM - Permutation Order Matters! 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 5 4 3 2 1 = 120 Shortcut! Factorial = ! on the calculator: Math, cursor to PRB or = A permutation of n objects taken r at a time... or =

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

a set of n objects taken r at a time without repetition 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

b. How many ways to get a committee of 3? 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!

Don’t forget about POW!! HW – 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 –