Counting Techniques Counting Techniques How many ways couldâ¦? There are 9 boys and 8 girls in the student council at Hermitage High School. How many ways could a single student be selected to hold a single office? There are 9+8=17 ways of making the selection The Addition Principle The events of selecting a boy and selecting a girl are called Mutually Exclusive or Disjoint. This is because a person cannot be both a boy and a girl. The Addition Principle How many ways can a die and a coin fall together? First make two Blanks _ _ Then write the number of possibilities for the die and the coin on the blanks. 6 2 Now multiply those numbers together to get 12. Fundamental Multiplication Principle Fundamental Multiplication Principle Suppose, from the 17 students in the student council, how many ways can you choose a president, secretary, and treasurer? One person cannot hold more than one position. If the president is elected first, how many options are there? 17 How many options are left for the secretary if that position is elected next? 16 Permutations Permutations Permutations Permutations A Combination is used to describe a selection of several objects where the order they were chosen does not matter. Think of the first two students entering the bus. If you only need to know who those first two students were and not the order. For example Brian then Darren would be the same as Darren then Brian. Combinations We knew there were 20 orders the first two student could enter the bus. For each pair of students there were two orders. How many combinations of the first two students can be made? Combinations Combinations Permutations: order matters Combinations: order does not, think groups If there are 8 students and 8 tests versions, how many ways can the tests be given out? 8!=40,320 How many two letter âwordsâ can be made from the word FLOWERS? 7P2=42 9 boys and 8 girls in student council. How many four person comities can consist of 3 boys and 1 girl? 9C3*8C1=84*8=672 Review