10/23/ Combinations

10/23/ Combinations Remember that Permutations told us how many different ways we could choose r items from a group of n items if the order mattered. The formula we used was:

10/23/ Combinations Combinations tell us how many ways we can pick r items from a group of n items if the order doesn’t matter. For example: If 10 people enter a contest where the first prize is $100, 2 nd is $75, and 3 rd is $50, then order matters – this is Permutations: If however, the three top prizes are $50 each, then the order doesn’t matter – this is now referred to as Combinations. Of the Three who finish, there are 6 different ways they can be arranged, but they are all the same combination of a winning set of people.

Combinations Formula: Are there more Combinations or Permutations? So, each combination of r items can be arranged in r! ways: Ex: 20 distinct points are chosen on a circle. chosen on a circle. a) How many segments can be formed? b) How many Triangles can be formed? 10/23/

Examples: At a restaurant, you can order pizza with any of 9 different toppings. How many different pizzas are possible with exactly 3 of these toppings? Five students from your class are randomly picked to be interviewed by the local newspaper. If your class contains 20 students, what is the probability that neither you nor your best friend will be picked? 10/23/