Unit 1 Day 2 Subsets Combinations and Pascals

Unit 1: Day 2 Subsets, Combinations, and Pascal’s Triangles Notes

Warm Up You and your friends have decided to go to Chic-fil-A for lunch, however your choice of menu items is limited. You can choose from the Original Sandwich, Waffle Fries, Salad, and Icedream Cone. Write down all of the possible orders (subsets) for the given items you have to choose from.

Examples: Subsets and Cardinality Example 1: List all of the subsets of set A = {1, 2, 3} How many subsets have a cardinality of 0? 1? 2? 3? Example 2: List all of the subsets of set B = {w, x, y, z} How many subsets have a cardinality of 0? 1? 2? 3? 4?

Examples Cont. Example 3: Given the set C = {Bobby, Cindy, Jan, Peter, Marsh, Greg} • How many subsets have a cardinality of 1? Have a cardinality of 5? • How many subsets have a cardinality of 2? Have a cardinality of 4? • How many subsets have a cardinality of 3? • How many subsets have a cardinality of 0? Have a cardinality of 6?

Total number of subsets…. If a set has n elements, n. Cr is the number of subsets with r elements.

Examples: Finding the number of subsets Example 4: Find the number of possible subsets in each. • How many 4 elements subsets does a set of 10 elements have? • How many 6 element subsets does a set of 13 elements have? • How many 3 elements subsets does a set of 21 elements have?

Examples Cont. • Example 5: List the subsets of each set: • { } • {1, 2}

Examples Cont. Example 6: q. The total number of subsets of a set with n elements is 2 n. q. The total number of proper subsets of a set with n elements is 2 n – 1. • What is the total number of subsets of a set with 6 elements? • What is the total number of subsets of a set with cardinality of 8? • What is the total number of proper subsets of a set with 5 elements? • If a set has a cardinality of 10, how many proper subsets would if have?