Algebra II Notes 3.3 The Counting Principle Number of Ways a Multipart Event Can Happen = number of ways each individual parts can happen. EX: A restaurant has 2 choices of appetizers, 3 main courses, and 4 desserts. How many different 3course meals can be made? In above example, you could also make a tree diagram. Factorial Notation = 4! = 4 x 3 x 2 x 1 = 24. In calculator: type in n value MATH PRB 4: ! EX: How many ways can 5 books be arranged on a shelf? EX: Find the value of 8! = 4! Notes 3.13 Methods of Counting Permutations – the number of ways a certain number of objects can be arranged when the order of arrangement matters. n Pr = n! where n is the total number of objects and r is the number for the subset. (n − r ) ! In calculator: type in n value MATH PRB 2: nPr type in r value. EX: How many 3-digit numbers can be created using the numbers 2, 3, 4, 5, 6 if the digits CANNOT be repeated? Combinations – the number of ways n objects can be arranged if order does NOT matter. n Cr = n! where n is the total number of objects and r is the number for the subset. r !⋅ (n − r )! In calculator: type in n value MATH PRB 3: nCr type in r value. EX: How many 3-topping pizzas can be created from 8 different topping choices?