Notes 9.1 – Basic Combinatorics. I. Types of Data 1.) Discrete Data – “Countable”; how many? 2.) Continuous Data – “uncountable”; measurements; you can.

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Presentation transcript:

Notes 9.1 – Basic Combinatorics

I. Types of Data 1.) Discrete Data – “Countable”; how many? 2.) Continuous Data – “uncountable”; measurements; you can always get a closer approximation.

II. The Counting Principle How many different ways can 5 friends stand in a line? How many different ways can 5 friends sit around a circular table?

III. Permutations A.) n items arranged in an order. permutations of 3-set. n! distinguishable permutation of an n-set.

B.) Ex. 1- A typical NJ License plate consist of 3 letters followed by 3 digits. How many possible plates are there if repeats of digits and letters are allowed? C.) Ex. 2- How many possible plates are there if repeats of digits and letters are not allowed?

D.) Ex. 3 - How many different 6 letter “words” can be formed by the word 1.) “VOLUME”?2.) “DABBLE”? E.) Ex. 4 - How many different11 letter “words” can be formed by the word “MISSISSIPPI”?

F.) Distinguishable Permutations- If an n-set contains n 1, n 2, …n k of a separate kind, then the number of permutations is

IV. Permutation Counting Formula A.) The number of permutations of n objects taken r at a time is given by the formula

B.) Ex. 5- Provide an algebraic expression equivalent to

V. Combinations A.) Use a COMBINATION anytime you are “selecting” or “choosing” an r-set of items from an n-set of items. NOTE: With combinations, order does not matter!!!

B.) Ex. 6 - How many different subcommittees of 4 people are possible if they are to be chosen from a group of 10 people? BE CAREFUL!!! Elected officials – Permutations; Committees- Combinations

C.) Subsets of an n-set : Ex. 7 - A pizzeria offers a choice of 10 toppings. How many possible pizzas are there if you order 4 toppings? D.) Ex. 8 - How many total possible pizzas are there?