body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

Big Ideas Math Geometry, 2014

BI

Big Ideas Math Geometry, 2014 View details

5. Permutations and Combinations

Continue to next subchapter

Exercise 32 Page 704

Recall the formula for a combination, _n C_r = n!/(n-r)! r!.

15 504

Practice makes perfect

To evaluate the given combination, we will use the corresponding formula. _n C_r = n!/(n-r)! r! We are given that n=20 and r=5. Let's substitute these values into the formula.

_n C_r = n!/(n-r)! r!

n= 20, r= 5

_(20) C_5 = 20!/( 20- 5)! 5!

Subtract term

_(20) C_5 = 20!/15! 5!

Write as a product

_(20) C_5 = 20* 19* 18* 17* 16* 15!/15! 5!

a/b=.a /15!./.b /15!.

_(20) C_5 = 20* 19* 18* 17* 16/5!

Write as a product

_(20) C_5 = 20* 19* 18* 17* 16/5* 4* 3* 2* 1

SplitIntoFactors

Split into factors

_(20) C_5 = 5* 4* 19* 3* 2* 3* 17* 16/5* 4* 3* 2* 1

CancelCommonFac

Cancel out common factors

_(20) C_5 = 5* 4* 19* 3* 2* 3* 17* 16/5* 4* 3* 2* 1

Simplify quotient

_(20) C_5 = 19* 3* 17* 16/1

a/1=a

_(20) C_5 = 19* 3* 17* 16

Multiply

_(20) C_5 = 15 504

Subchapter links

Communicate Your Answer p.699

Monitoring Progress p.700-703

Exercises p.704-706