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Notes 9.1 – Basic Combinatorics

Learn the fundamentals of discrete and continuous data, counting principles, permutations, and combinations in combinatorics. Understand how to calculate permutations of items, distinguishable arrangements, and possibilities like forming words or selecting subsets. Dive into permutation counting formulas and practical examples to enhance your problem-solving skills.

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Notes 9.1 – Basic Combinatorics

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  1. Notes 9.1 – Basic Combinatorics

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

  3. 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?

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

  5. 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?

  6. 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”?

  7. F.) Distinguishable Permutations- If an n-set contains n1, n2, …nkof a separate kind, then the number of permutations is

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

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

  10. 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!!!

  11. 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

  12. 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?

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