Assignment 16 (2A.2.3) Homework: Pg.46 (5-10) Warm Up Factor (take out the greatest common factor first) a. 3 ! + 24 b. 12 ! − 75 ! c. 32 ! + 18 Notes Factorials (n!) tell you to multiply all the descending integers from n. examples: 5! = 5 ∙ 4 ∙ 3 ∙ 2 ∙ 1 3! = 3 ∙ 2 ∙ 1 0! = 1 Counting Principles: Permutations are arrangements of items in a particular order. n P r = !! !!! ! gives you the number of ways you arrange r items from a set of n. example: If there are 8 different countries in the final Olympic event, then there are 8 P 3 ways the medals can be awarded. 8 P 3 = !! !!! ! = !∙!∙!∙!∙!∙!∙!∙! !∙!∙!∙!∙! = 8 ∙ 7 ∙ 6 = 336 Combinations are arrangements of items which order does not matter. n C r = !! !! !!! ! gives you the number of ways you can group r items from a set of n. example: If there are 38 students in the class, then there are 38 C 4 ways to make groups of 4. 38 C 4 = !"! !!!"! = !"∙!"∙!"∙!" !∙!∙!∙! = 73,815