How Do You Do Permutations and Combinations in Desmos?

If you do not have a calculator that does combinations or permutations, there is another option to do those calculation. Desmos is know for its ability to graph formulas…but did you know it can also do calculations like a scientific calculator?

To find this scientific calculator, go to the Desmos website (

Located in the bottom left corner of the screen is a button to access the scientific calculator.Pressing this button takes you to the calculator. To access the command for permutations, press the button for func highlighted below.

This will take you to a new set of buttons. Select the button nPr shown below.

Pressing this button will paste the permutation command to the line above the buttons.

If you are computing 6P4 (or P(6,4)), you need to use your keyboard to type 6,4).

You can also do combinations in a similar manner.

If you type the carriage return on the keypad (dark blue button on the bottom right), it will go to a line on which you can put a new command.

To do a factorial like 10!, type in the number 10 on the keyboard.

Then select the ! button.

Notice that there are also other buttons that might prove useful like a square root, nth root, natural logarithm, and common logarithm buttons.

How Do I Use WolframAlpha To Graph a Formula?

A number of you have asked me about alternatives to a TI graphing calculator. In addition to Excel, there are many online graphing tools available. If you have an Android phone or IPhone, there are a huge number of free apps that are available. I have had a hard time finding just one that does everything we need. Most will graph formulas, but may or may not graph data and fit data to lines. None of them work identically to a graphing calculator which makes them difficult to support. But luckily there is another option!

Another option is the website WolframAlpha ( This website is the Internet’s leading computational engine. It can do just about anything. The trouble is knowing how to use it to do just about anything.

When you go to this website, you’ll see a box in which you can enter commands to help you do mathematics. The list of things you can do is HUGE. It is best to show some examples to get you started.

For instance, suppose you want to graph the function y = -5.686x + 676.173 in a window from x = 0 to x = 25. Enter the text you see below into WolframAlpha followed by Enter.

WolframAlpha makes a nice graph. If you want to graph two formulas simultaneously, add another formula with the word “and” as you see below.

You can see that these lines are going to meet. To see this point of intersection, extend the graph by modifying the input to WolframAlpha as you see below.

We can find this point of intersection by modifying the input to WolframAlpha with the command “intersections”:

Not only does it give a decimal…it also gives the exact answer in terms of fractions!

Often you are interested in evaluating the model above at a particular point. We can do this by clicking on the formula above. This will make WolframAlpha graph the formula by itself. Now add “where x = 20” on the command line and you will see:

This gives the same output as TRACE on a graphing calculator. I’ll continue to make posts about WolframAlpha so those of you who do not have access to a graphing calculator have an alternative way to make graphs, calculate values, ect.