Learning Objectives: . Solve counting problems using various methods . Find the number of permutations of n distinct objects using the multiplication principle . Find the number of permutations of n non-distinct objects . Find the number of permutations of n distinct objects using the formula . Find the number of combinations using the formula Problem #1 Celina is picking a new frame for a custom piece of artwork. She has to select a frame size, material, and color. There are four different frame sizes, three different frame materials, and six different frame colors. She must chose one option only from each category. How many different possible frames could Celina pick from? Problem #2 There are 15 candidates running for any of 5 distinct positions on the local school board. In how many different ways could the 5 positions be filled? Problem #3 I have 15 outfits to select from to pack for my business trip. I would like to select three of them to pack in my suitcase. How many packing possibilities are there? Page 1 of 2