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# Permutation Problems

## Using the nPr function found in the Math menu under PRB  on the TI calculator

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Practice Permutation Problems

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Permutation Problems

Suppose you want to select items to place on your shelf at home from left to right. If you have 45 items from which to select how many possible arrangements can you make? Can you see why a calculator might be useful to find this answer?

### Guidance

To calculate permutations (nPr\begin{align*}nPr\end{align*}) on the TI calculator, first enter the n\begin{align*}n\end{align*} value, and then press MATH\begin{align*}\boxed{\text{MATH}}\end{align*}. You should see menus across the top of the screen. You want the fourth menu: PRB (arrow right 3 times). The PRB menu should appear as follows:

You will see several options, with nPr\begin{align*}nPr\end{align*} being the second. Press 2\begin{align*}\boxed{2}\end{align*}, and then enter the r\begin{align*}r\end{align*} value. Finally, press ENTER\begin{align*}\boxed{\text{ENTER}}\end{align*} to calculate the answer.

#### Example A

Compute 9P5\begin{align*}{_9}P_5\end{align*} using your TI calculator.

\begin{align*}\boxed{9} \ \boxed{\text{MATH}} \ \boxed{\blacktriangleright} \ \boxed{\blacktriangleright} \ \boxed{\blacktriangleright} \ (\text{PRB}) \ \boxed{2} \ (\text{nPr}) \ \boxed{5} \ \boxed{\text{ENTER}}\end{align*}

After pressing \begin{align*}\boxed{\text{ENTER}}\end{align*}, you should see the following on your calculator's screen:

Therefore, \begin{align*}{_9}P_5= 15,120\end{align*}. That is, there are 15,120 unique ways to arrange/list five ojects out of a possilble nine from which to choose.

#### Example B

In how many ways can first and second place be awarded to 10 people? Compute the answer using your TI calculator.

There are 10 people \begin{align*}(n = 10)\end{align*}, and there are 2 prize winners \begin{align*}(r = 2)\end{align*}, so to find the answer, enter the following into your TI calculator:

\begin{align*}\boxed{10} \ \boxed{\text{MATH}} \ \boxed{\blacktriangleright} \ \boxed{\blacktriangleright} \ \boxed{\blacktriangleright} \ (\text{PRB}) \ \boxed{2} \ (\text{nPr}) \ \boxed{2} \ \boxed{\text{ENTER}}\end{align*}

After pressing \begin{align*}\boxed{\text{ENTER}}\end{align*}, you should see the following on your calculator's screen:

Therefore, \begin{align*}{_{10}}P_2= 90\end{align*}, which means that the number of ways that first and second place can be awarded to 10 people is 90.

#### Example C

In how many ways can 3 favorite desserts be listed in order from a menu of 10? Compute the answer using your TI calculator.

There are 10 menu items \begin{align*}(n = 10)\end{align*}, and you are choosing 3 favorite desserts \begin{align*}(r = 3)\end{align*} in order, so to find the answer, enter the following into your TI calculator:

\begin{align*}\boxed{10} \ \boxed{\text{MATH}} \ \boxed{\blacktriangleright} \ \boxed{\blacktriangleright} \ \boxed{\blacktriangleright} \ (\text{PRB}) \ \boxed{2} \ (\text{nPr}) \ \boxed{3} \ \boxed{\text{ENTER}}\end{align*}

After pressing \begin{align*}\boxed{\text{ENTER}}\end{align*}, you should see the following on your calculator's screen:

Therefore, \begin{align*}{_{10}}P_3= 720\end{align*}, which means that the number of ways that 3 favorite desserts can be listed in order from a menu of 10 is 720.

### Vocabulary

When calculating permutations with the TI calculator, the \begin{align*}n\end{align*} value is the number of objects from which you are choosing, and the \begin{align*}r\end{align*} value is the number of objects chosen.

### Practice

1. Enter each of the following sets of keystrokes into your TI calculator to compute the corresponding permutations.
2. \begin{align*}\boxed{1} \ \boxed{2} \ \boxed{\text{MATH}} \ \boxed{\blacktriangleright} \ \boxed{\blacktriangleright} \ \boxed{\blacktriangleright} \ (\text{PRB}) \ \boxed{2} \ (\text{nPr}) \ \boxed{8} \ \boxed{\text{ENTER}}\end{align*}
3. \begin{align*}\boxed{1} \ \boxed{5} \ \boxed{\text{MATH}} \ \boxed{\blacktriangleright} \ \boxed{\blacktriangleright} \ \boxed{\blacktriangleright} \ (\text{PRB}) \ \boxed{2} \ (\text{nPr}) \ \boxed{5} \ \boxed{\text{ENTER}}\end{align*}
4. \begin{align*}\boxed{2} \ \boxed{0} \ \boxed{\text{MATH}} \ \boxed{\blacktriangleright} \ \boxed{\blacktriangleright} \ \boxed{\blacktriangleright} \ (\text{PRB}) \ \boxed{2} \ (\text{nPr}) \ \boxed{7} \ \boxed{\text{ENTER}}\end{align*}
5. \begin{align*}\boxed{1} \ \boxed{1} \ \boxed{\text{MATH}} \ \boxed{\blacktriangleright} \ \boxed{\blacktriangleright} \ \boxed{\blacktriangleright} \ (\text{PRB}) \ \boxed{2} \ (\text{nPr}) \ \boxed{6} \ \boxed{\text{ENTER}}\end{align*}
6. \begin{align*}\boxed{1} \ \boxed{4} \ \boxed{\text{MATH}} \ \boxed{\blacktriangleright} \ \boxed{\blacktriangleright} \ \boxed{\blacktriangleright} \ (\text{PRB}) \ \boxed{2} \ (\text{nPr}) \ \boxed{4} \ \boxed{\text{ENTER}}\end{align*}
7. \begin{align*}\boxed{1} \ \boxed{9} \ \boxed{\text{MATH}} \ \boxed{\blacktriangleright} \ \boxed{\blacktriangleright} \ \boxed{\blacktriangleright} \ (\text{PRB}) \ \boxed{2} \ (\text{nPr}) \ \boxed{3} \ \boxed{\text{ENTER}}\end{align*}
8. \begin{align*}\boxed{2} \ \boxed{2} \ \boxed{\text{MATH}} \ \boxed{\blacktriangleright} \ \boxed{\blacktriangleright} \ \boxed{\blacktriangleright} \ (\text{PRB}) \ \boxed{2} \ (\text{nPr}) \ \boxed{9} \ \boxed{\text{ENTER}}\end{align*}
9. \begin{align*}\boxed{1} \ \boxed{8} \ \boxed{\text{MATH}} \ \boxed{\blacktriangleright} \ \boxed{\blacktriangleright} \ \boxed{\blacktriangleright} \ (\text{PRB}) \ \boxed{2} \ (\text{nPr}) \ \boxed{2} \ \boxed{\text{ENTER}}\end{align*}
10. \begin{align*}\boxed{2} \ \boxed{5} \ \boxed{\text{MATH}} \ \boxed{\blacktriangleright} \ \boxed{\blacktriangleright} \ \boxed{\blacktriangleright} \ (\text{PRB}) \ \boxed{2} \ (\text{nPr}) \ \boxed{3} \ \boxed{\text{ENTER}}\end{align*}
11. \begin{align*}\boxed{1} \ \boxed{6} \ \boxed{\text{MATH}} \ \boxed{\blacktriangleright} \ \boxed{\blacktriangleright} \ \boxed{\blacktriangleright} \ (\text{PRB}) \ \boxed{2} \ (\text{nPr}) \ \boxed{6} \ \boxed{\text{ENTER}}\end{align*}

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