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Big Ideas Math Geometry, 2014

BI

Big Ideas Math Geometry, 2014 View details

5. Permutations and Combinations

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Exercise 30 Page 704

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

330

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=11 and r=4. Let's substitute these values into the formula.

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

n= 11, r= 4

_(11) C_4 = 11!/( 11- 4)! 4!

Subtract term

_(11) C_4 = 11!/7! 4!

Write as a product

_(11) C_4 = 11* 10* 9* 8* 7!/7! 4!

a/b=.a /7!./.b /7!.

_(11) C_4 = 11* 10* 9* 8/4!

Write as a product

_(11) C_4 = 11* 10* 9* 8/4* 3* 2* 1

SplitIntoFactors

Split into factors

_(11) C_4 = 11* 10* 3* 3 * 4 * 2/4* 3* 2* 1

CancelCommonFac

Cancel out common factors

_(11) C_4 = 11* 10* 3* 3* 4* 2/4* 3* 2* 1

Simplify quotient

_(11) C_4 = 11* 10* 3/1

a/1=a

_(11) C_4 = 11* 10* 3

Multiply

_(11) C_4 = 330

Subchapter links

Communicate Your Answer p.699

Monitoring Progress p.700-703

Exercises p.704-706