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Pearson Geometry Common Core, 2011

PG

Pearson Geometry Common Core, 2011 View details

3. Permutations and Combinations

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Exercise 15 Page 841

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

210

Practice makes perfect

To evaluate the given combination, we will use the corresponding formula. _n C_r = n!/r!(n-r)! We are given that n=10 and r=6. Let's substitute these values into the formula.

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

n= 10, r= 6

_(10) C_6 = 10!/6!( 10- 6)!

Subtract term

_(10) C_6 = 10!/6!4!

Write as a product

_(10) C_6 = 10* 9* 8* 7* 6* 5* 4* 3* 2* 1/(6* 5* 4* 3* 2* 1)(4* 3* 2* 1)

CancelCommonFac

Cancel out common factors

_(10) C_6 = 10* 9* 8* 7* 6* 5* 4* 3* 2* 1/(6* 5* 4* 3* 2* 1)(4* 3* 2* 1)

Simplify quotient

_(10) C_6 = 10* 9* 8* 7/4* 3* 2* 1

▼

Simplify

SplitIntoFactors

Split into factors

_(10) C_6 = 10* 3* 3* 4* 2* 7/4* 3* 2* 1

CancelCommonFac

Cancel out common factors

_(10) C_6 = 10* 3* 3* 4* 2* 7/4* 3* 2* 1

Simplify quotient

_(10) C_6 = 10* 3* 7/1

a/1=a

_(10) C_6 = 10* 3* 7

Multiply

_(10) C_6 = 210

There are 210 combinations.

Alternative Solution

Using the calculator

We can evaluate the number of combinations _(10)C_6 by using the graphic calculator. To do so, we have to start by entering the number of items, which is equal to 10.

Next, we push MATH and scroll right until we reach PRB. Then, we scroll down to the third row and push ENTER.

window of a TI83 graphing calculator

window of a TI83 graphing calculator

Finally, by entering the number of items to be chosen and hitting ENTER, we can calculate the number of combinations.

Subchapter links

Lesson Check p.840

Practice and Problem-Solving Exercises p.841-842

Standardized Test Prep p.842

Mixed Review p.842