1. Permutations Prof. Islam Combinatorics Lesson 5

2. Warm Up  Here are the number of elements in three different sets. Without a calculator express in exponential notation the total number of combinations for these sets. Then find the square root of that number.  l125l xl140l x l100l x l28l=

3. Warm Up-Student Work

4. The Math  l125l xl140l x l100l x l28l=

5. Student Work

6. What is the square root of the number?  Sqr. Rt. = l125l xl140l x l100l x l28l= First: express each number in it’s factored form with exponents. (5^3) x (7 x 5 x 2^2) x (5^2 x 2^2) x (7 X 2^2) = 7^2 x 5^6 x 2^6 Now take the square root of that number The Square root = 7 x 5^3 x 2^3 This is an easier number to multiply Now multiply it out = 125 x 56 = 7000 Now square that number and you get 49,000,000 Or 4.9 x 10 ^7 in scientific notation. You have been taught all the knowledge to do this in the past two years!

7. Now square it  The square root = 7000  The square =49000000  Now express this in scientific notation:  4.9 x 10^7

8. Spore Game  www.spore.com www.spore.com  In the game you have a lot more options than you had in the homework  Watch and write down some categories.

9. Let’s List some categories Then assume a number of choices for each

10. Ordered Arrangement ABCD body typesSets of EyesMouthsNoses HairyOne eyebigcute ScalesTwo eyessmalllong FeathersThree eyes Green Skin

11. You have to put only one type on each alien. How many ways can you do this? A={Hairy, Scales, Feathers, Green Skin}

12. Practice  Using 5 Colored Tiles. How many ways can you fill each slot? ______ ______ _______ ______ _______ ______ ______ _______ ______ _____ ______ _______ ____ _____ _____

13. Factorial !

14. Permutation  No item is used more than once  The order of the arrangement matters  Formula for Permutations is: Permutation of n things taken r at a Time The number of possible permutation of if r items are taken from n items is nPr = n!/(n-r)!