PERMUTATIONS AND COMBINATIONS/FUNCTION NOTATION AND OPERATIONS Formulae P n r 1. n! n r ! C n r n! r ! n r ! tk 1 C a n k nk k b There are 6 boys and 8 girls in a group of students a) Calculate the number of ways that a president, vice-president and treasurer can be selected. a) __________________________ 2 marks b) Calculate the number of ways that a committee of 3 students which has at least 1 girl can be selected from the group. b) __________________________ 2. A car license plate consists of 6 characters. a) The first 3 characters are letters excluding I, O, Q and U. The last 3 characters are any of the numerals 0 to 9 inclusive. How many different license plates are possible? a) __________________________ b) The first 2 characters are any letter. The last 4 characters are odd numbers from 1 to 9 inclusive. How many different license plates are possible. th 10 1 term of 3 x y . 2 3. What is the 8 4. Solve the following equations algebraically for n . Show your working using factorial notation. a) n! 12 3! n 2 ! a) __________________________ b) P 6720 8 n b) __________________________ 5. Given the graphs of f x and g x find f g 1 . 5. __________________________ 6. 1 2 Prove algebraically that f x 3x 2 and g x x are inverses of each other. 3 3 7. Given: f g x 4 x 5 and f g x 6 x 3 find f x and g x algebraically. 7. __________________________ 1 x and g x 1 . 2x 5 2 Determine g o f x then sketch the graph of g o f x on the grid provided. 8. Given the graphs of f x Y 5 -5 X 5 -5 2 marks 8. __________________________