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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 5 Page 840

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

15

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=6 and r=2. Let's substitute these values into the formula.

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

n= 6, r= 2

_6 C_2 = 6!/2!( 6- 2)!

Subtract term

_6 C_2 = 6!/2! 4!

Write as a product

_6 C_2 = 6* 5* 4* 3* 2* 1/(2* 1)( 4* 3* 2* 1)

CancelCommonFac

Cancel out common factors

_6 C_2 = 6* 5* 4* 3* 2* 1/(2* 1)( 4* 3* 2* 1)

Simplify quotient

_6 C_2 = 6* 5/2* 1

Multiply

_6 C_2 = 6* 5/2

a/b=.a /2./.b /2.

_6 C_2 = 3* 5/1

a/1=a

_6 C_2 = 3* 5

Multiply

_6 C_2 = 15

There are 15 combinations.

Alternative Solution

Using the calculator

We can evaluate the number of combinations _6C_2 by using the graphic calculator. To do so, we have to start by entering the number of items, which is equal to 6.

Next, we push MATH and then scroll right until we reach PRB. Then, 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