Permutations

Prof. IslamCombinatorics Lesson 5

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=

Warm Up-Student Work

The Math l125l xl140l x l100l x l28l=

Student Work

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 numberThe Square root = 7 x 5^3 x 2^3This is an easier number to multiplyNow multiply it out = 125 x 56 = 7000Now square that number and you get 49,000,000Or 4.9 x 10 ^7 in scientific notation.You have been taught all the knowledge to do this in the past

two years!

Now square it The square root = 7000

The square =49000000

Now express this in scientific notation: 4.9 x 10^7

Spore Game www.spore.com In the game you have a lot more options

than you had in the homework Watch and write down some categories.

Let’s List some categoriesThen assume a number of choices for each

Ordered Arrangement

A B C D

body types Sets of Eyes

Mouths Noses

Hairy One eye big cute

Scales Two eyes small long

Feathers Three eyes

Green Skin

You have to put only one type on each alien. How many ways can you do this?

A={Hairy, Scales, Feathers, Green Skin}

Practice Using 5 Colored Tiles. How many ways can

you fill each slot?____________ _____________ _______ ______ ______ _______ ______ ___________ _______ ____ _____ _____

Factorial

!

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)!