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Pearson Geometry Common Core, 2011

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Pearson Geometry Common Core, 2011 View details

Mid-Chapter Quiz

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Exercise 13 Page 843

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

56

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=8 and r=5. Let's substitute these values into the formula.

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

n= 8, r= 5

_8 C_5 = 8!/5!( 8- 5)!

Subtract term

_8 C_5 = 8!/5! 3!

Write as a product

_8 C_5 = 8* 7* 6* 5* 4* 3* 2* 1/(5* 4* 3* 2* 1)(3* 2* 1)

CancelCommonFac

Cancel out common factors

_8 C_5 = 8* 7* 6* 5* 4* 3* 2* 1/(5* 4* 3* 2* 1)(3* 2* 1)

Simplify quotient

_8 C_5 = 8* 7* 6/3* 2* 1

Multiply

_8 C_5 = 336/6

Calculate quotient

_8 C_5 = 56

There are 56 combinations.

Alternative Solution

Using the calculator

We can evaluate the number of combinations _8C_5 using the graphic calculator. To do so, we have to start by entering the number of items, which is equal to 8.

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.