2. Quit

3. Permutations Combinations Pascal’s triangle Binomial Theorem

4. Quit These are arrangements in which the order matters. Consider three letters a, b, c. How many arrangements of these three letters can be made using each once? There are six possible arrangements of three letters: abc acb bac bca cab cba = 6 permutations Permutations P 3 3 = 3  2  1 = 6

5. Quit How many arrangements of two letters can be made from three letters? ab ac ba bc ca cb = 6 permutations How many arrangements of one letter can be made from three letters? a b c = 3 permutations Permutations P 3 2 = 3  2 = 6 P 3 1 = 3= 3

6. Quit F SITR Permutations How many arrangements of five letters can be made from the letters in the word FIRST?  5 24 13 P 5 5 = 5  4  3  2  1 = 120

7. QuitCombinations These are groups of things where order does not matter. Consider three letters a, b, c. How many combinations of three letters can be made taking each once? There is only 1, abc = 1 combination C 3 3 = 1= 1

8. QuitCombinations How many combinations of two letters can be made from three letters? ab, ac, bc = 3 combinations How many combinations of one letter can be made from three letters? a, b, c = 3 combinations C 3 2 = 3= 3 C 3 1 = 3= 3

9. QuitCombinations Fred has a voucher to pick any two of the top 10 PS3 games! How many different combinations of 2 games can he pick? C 10 2 = 45 10  9 2  1 ––––– =

10. Quit 1 1 1 1 1 2 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 Pascal’s Triangle

11. Quit Binomial Theorem 1 1 1 1 1 2 1 3 3 1 1 4 6 4 1 (x + y)1 = x + y(x + y)1 = x + y (x + y) 2 = x 2 + 2xy + y 2 (x + y)3 = x3 + 3x2y1 + 3x1y2 + y3(x + y)3 = x3 + 3x2y1 + 3x1y2 + y3 (x + y)4 = x4 + 4x3y1 + 6x2y2 + 4x1y3 + y4(x + y)4 = x4 + 4x3y1 + 6x2y2 + 4x1y3 + y4

12. Quit x 5 y 1 6 Binomial Theorem (x + y)6(x + y)6 6 C 0 x 6 6 C 1 6 C 2 x 4 y 2 + + 6 C 3 x 3 y 3 + 6 C 4 x 2 y 4 + 6 C 5 x 1 y 5 + 6 C 6 y 6 +1520156x 6 + 6x 5 y 1 + 15x 4 y 2 + 20x 3 y 3 + 15x 2 y 4 + 6x 1 y 5 + y 6

13. YesNo Do you want to end show?