Pearson Geometry Common Core, 2011
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Pearson Geometry Common Core, 2011 View details
3. Permutations and Combinations
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Exercise 6 Page 840

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

20

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=3. Let's substitute these values into the formula.
_n C_r = n!/(n-r)! r!
_6 C_3 = 6!/3!( 6- 3)!
_6 C_3 = 6!/3! 3!

Write as a product

_6 C_3 = 6* 5* 4* 3* 2* 1/(3* 2* 1)(3* 2* 1)
_6 C_3 = 6* 5* 4* 3* 2* 1/(3* 2* 1)(3* 2* 1)
_6 C_3 = 6* 5* 4/3* 2* 1
_6 C_3 = 120/6
_6 C_3 = 20
There are 20 combinations.

Alternative Solution

Using the calculator

We can evaluate the number of combinations _6C_3 using the graphic calculator. To do so, we have to start by entering the number of items, which is equal to 6.

window of a TI83 graphing calculator

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.

window of a graphing calculator