1. Counting Principle part 2 I. Math symbols and formulas for Counting Principles. A) Basic Counting Principle = m x n where you have m things and n things and want them arranged every possible way. B) Combinations (counting principle) where order does NOT matter. It comes from the Permutations formula. 1) If repeating is NOT allowed (like a lottery ticket) 2) If repeating IS allowed (like a combination lock) n = number of objects in the set r = how many objects we are selecting/arranging. ! = factorial MENU  5 Probability  1 Factorial

2. Counting Principle part 2 Examples: Combinations without repeating 1) How many ways can you create a password that uses 5 different lower case letters in a row. 2) If a lottery ticket has 59 numbers and you have to pick 5 of them, how many different ways can you fill out a lottery ticket? This does not include picking the powerball (1 number out of 36).

3. Counting Principle part 2 C) If the objects are NOT allowed to be repeated, then you can use a button on the calculator to find how many combinations (counting principle) there are. ( nCr ) 1) MENU  5 Probability  3 Combinations nCr(n,r) n = number of objects r = how many are being selected. Examples: 1b) A 5 letter lower case password (no repeating). n = 26 & r = 5 type MENU  5  3 type 26,5 in the ( ) Screen shows nCr(26,5) the answer is 65780. 2b) A 59 number lottery ticket, pick 5 numbers. n = 59 & r = 5 nCr(59,5) = 5,006,386

4. Counting Principle part 2 Examples: Combinations with repeating. 3) How many ways can you create a password that uses any 5 lower case letters? (repeating is allowed) Note: There is NOT a button to do repeating combinations. You have to use the formula.