Warm Up Make your own burrito. Choice of Flour or Corn tortilla

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Warm Up Make your own burrito. Choice of Flour or Corn tortilla Choice of Beef, Chicken, or Barbacoa Choice of Veggies, Beans, Salsa, Lettuce How many different burrito options are there?

Section 3.4 Notes Counting Principles

Fundamental Counting Principle If one event can occur in x number of ways and a second event can occur in y number of ways, the number of ways in which two events can occur in sequence is xy. Ex. 1 4 different breakfast options 3 different lunch options How many different breakfast and lunch options are available? 4 * 3 = 12 different options

Example 1 There are 7 students competing in an academic decathlon. How many different orders can the students finish in terms of first to last place?

Example 2 Cell phone security code. How many different options are there?

More examples of the fundamental counting principle on Page 140

Warm Up A student has 6 pairs of shoes, 8 pairs of pants and 10 dress shirts. How many different outfits can the students create I may collect it today?

Warm Up An Access code to a home security system needs a six digit code, there are two restrictions, the first number must be a 1, 2 or 3 and the second number must be a 1. How many possible options for the code exist? I will either collect warm-ups today or tomorrow.

Section 3.4 Notes (Part 2) Counting Principles

Permutation of n objects Is an ordered arrangement of objects (order matters). The number of different permutations of n distinct (different) objects is n!. (All options are used) n! = n * (n-1) * ( n-2 ) * ( n-3) … 3 * 2 * 1 4! = 4 * 3 * 2 *1 = 24 8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40320

Permutation Example 1 The Golden West league consists of 6 different baseball teams (Orange, Santa Ana, Westminster, Ocean View, Loara and Segerstrom). How many different final standings are possible.

More examples of permutations on page 142

Permutations of n Objects Taken r At A Time Suppose you want to use some objects (r) of a group (n) and put them in order. (all objects are not used) n = total objects in group r = number of objects that you want to pull out

Example #1 There are 14 cars that are racing, how many different ways can they finish in first, second and third place. Assume there are no ties.

Combinations Order does not matter, not all options have to be used. n = all objects in a group r = number of objects that you want to pull out

Combination Example Four out of 30 students are selected from each Statistics class to go to Magic Mountain. How many different ways can the four students be selected?

More Combination Examples On page 145

Warm Up In a race of 6 cars. In how many different ways can they finish in first, second and third place?

Distinguishable Permutations Section 3.4 Notes (Part 3) Distinguishable Permutations

Distinguishable Permutations Distinguishable Permutations are used when some objects in the group are the same. The key word in these problems will be distinguishable.

Example 1 In how many distinguishable ways can you arrange the letters in knickknack?

More examples On page 143 and 144