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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 3 Page 840

To evaluate the given permutation, we will use the corresponding formula.

_{n} P_{r} = \frac{n !}{( n - r ) !}

We are given that

n = 6

and

r = 2 .

Let's substitute these values into the formula.

_{n} P_{r} = \frac{n !}{( n - r ) !}

$n = 6$ , $r = 2$

_{6} P_{2} = \frac{6 !}{( 6 - 2 ) !}

Subtract term

_{6} P_{2} = \frac{6 !}{4 !}

Write as a product

_{6} P_{2} = \frac{6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{4 \cdot 3 \cdot 2 \cdot 1}

CancelCommonFac

Cancel out common factors

_{6} P_{2} = \frac{6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{4 \cdot 3 \cdot 2 \cdot 1}

Simplify quotient

_{6} P_{2} = \frac{6 \cdot 5}{1}

$\frac{a}{1} = a$

_{6} P_{2} = 6 \cdot 5

Multiply

_{6} P_{2} = 30

There are

30

permutations.

Alternative Solution

Using the calculator

We can evaluate the number of permutations $_{6} C_{2}$ 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 $M A T H$ and scroll right until we reach PRB. Then, we scroll down to the second row and push $E N T E R .$

window of a TI83 graphing calculator

window of a TI83 graphing calculator

Finally, by entering the number of items to be chosen and hitting $E N T E R,$ we can calculate the number of permutations.

Subchapter links

Lesson Check p.840

Practice and Problem-Solving Exercises p.841-842

Standardized Test Prep p.842

Mixed Review p.842