MTH 231 Lecture Notes - Lecture 20: Multiset, Subset, If And Only If

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orchidpig108

20 Jul 2018

School

Oregon State University

Department

Mathematics

Course

MTH 231

Professor

All

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Document Summary

* side note: planning more restriction on team rests in the more possibilities. Ex how many ways can you chose these (cid:886) if z are offense (cid:886) (cid:884) are defense (cid:2872) (cid:2871) (cid:2870) (cid:2869)=(cid:883)(cid:882) (cid:885) (cid:889)=(cid:884)(cid:883)(cid:882) (cid:4672)(cid:2869)(cid:2868)(cid:2872)(cid:4673)=(cid:2869)(cid:2868)!(cid:2872)! (cid:2874)!=(cid:2869)(cid:2868) (cid:2877) (cid:2876) (cid:2875) (cid:2874)! (cid:2872)!(cid:2874)! =(cid:883)(cid:882) (cid:891) (cid:889) (cid:884) ((cid:883)(cid:882)(cid:886))((cid:886)(cid:884))= (cid:883)(cid:882)(cid:886)! (cid:888): (cid:886)(cid:884)! (cid:888)!= (cid:883)(cid:882)! (cid:884)!(cid:884)! (cid:888)! Ex: (cid:4672)(cid:2871)(cid:2870)(cid:4673)= (cid:2871)!(cid:2870)!(cid:2869)!=(cid:2871) (cid:2870)!(cid:2870)! (cid:2869)!=(cid:885) (cid:4672) (cid:2871)(cid:2871) (cid:2870)(cid:4673)=(cid:4672)(cid:2871)(cid:2869)(cid:4673)= (cid:2871)(cid:2869)!(cid:2870)!=(cid:2871). (cid:2870)!(cid:2870)! (cid:2869)!=(cid:885) Proof (cid:4672) (cid:4673)= (cid:4666) (cid:4667)! (cid:4666) (cid:4667)! (cid:4672)(cid:3051)(cid:3052)(cid:4673)= (cid:3051)! (cid:4666) (cid:4667)! (cid:4666) +(cid:4667)!= ! (cid:3052)! (cid:4666)(cid:3051) (cid:3052)(cid:4667)!= (cid:1853) (cid:1854) (cid:1855) (cid:885)! (cid:1853) (cid:1854) (cid:1854) for each of the (cid:885)! Ways that you each order (cid:1853) (cid:1854) (cid:1855)(cid:1853) (cid:1855) (cid:1854) (cid:883)[(cid:1853)(cid:1853)(cid:1854)(cid:1854)(cid:1854)(cid:1854) same =(cid:2871)! (cid:2870)!=(cid:885) (cid:1853) (cid:1854) (cid:1854),(cid:884)! Of the ways you order the (cid:1855) (cid:1853) (cid:1854)(cid:1854) (cid:1853) (cid:1855) (cid:884)[ (cid:1854) (cid:1853) (cid:1854)(cid:1854) (cid:1853) (cid:1854) same the (cid:1854) (cid:1871) /(cid:1867) changing the world (cid:1855) (cid:1854) (cid:1853)(cid:1854) (cid:1855) (cid:1853) (cid:885)[(cid:1854) (cid:1854) (cid:1853) (cid:1854) (cid:1854) (cid:1853) same. Ex: permute (cid:1853) (cid:1853) (cid:1853) (cid:1854) (cid:1855)=(cid:2873)! (cid:2871)!

Related Questions

1) What is the total amount of your purchase if you bought 5 sweaters for $X and 2 additional sweatersat 50% off ?

$5X

$6X

$7.5X

$10X

2. Formula for the distance (d) is given by d = rate*time. For example if you are traveling at 60 mph for 3 hours the distance traveled is 180 (=60*3). Assuming Mary is traveling at 50 mph and Jim is traveling at 60 mph, how long does Jim have to travel in order that the distance between Mary and Jim is greater than or equal to 100 miles? NOTE: After one hour Jim is 10 miles ahead

Assume Mary and Jim leave at the same time, are traveling in the same direction on parallel tracks

11 hours

9 hours

10 hours

8 hours

3.Julie buys 10 CDs for $20. If DVDs cost $2 more, how many DVDs can she buy for the same 20 dollars?Hint: How much each CD cost?

4.125% of a certain number equals 35. What is the number?