Geometry permutations and combinations worksheet

The whole topic is one question: does the order matter. Permutations count arrangements, combinations count selections, and the only difference in the arithmetic is dividing by the number of ways the chosen ones could be shuffled.

Select your difficulty

Pick more than one for a sheet that mixes them.



Sigma Prep · sigmaprep.io/worksheets Name Permutations and Combinations Date Period Evaluate each expression. $_{13} P_{2}$ $_{13} C_{4}$ $_{14} P_{2}$ $_{13} C_{3}$ $_{12} P_{3}$ $_{12} C_{2}$ $_{13} P_{4}$ $_{12} C_{3}$ $_{12} P_{2}$ $_{14} C_{2}$ $_{14} P_{3}$ $_{14} C_{4}$ $_{12} P_{4}$ $_{13} C_{2}$ $_{14} P_{4}$ $_{14} C_{3}$ $_{13} P_{3}$ $_{12} C_{4}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Permutations and Combinations

Date Period

Evaluate each expression.

$_{13} P_{2}$
$_{13} C_{4}$
$_{14} P_{2}$
$_{13} C_{3}$
$_{12} P_{3}$
$_{12} C_{2}$
$_{13} P_{4}$
$_{12} C_{3}$
$_{12} P_{2}$
$_{14} C_{2}$
$_{14} P_{3}$
$_{14} C_{4}$
$_{12} P_{4}$
$_{13} C_{2}$
$_{14} P_{4}$
$_{14} C_{3}$
$_{13} P_{3}$
$_{12} C_{4}$



Sigma Prep · sigmaprep.io/worksheets Name Permutations and CombinationsAnswer keyVersion 1 Date Period Evaluate each expression. $_{13} P_{2}$ $156$ $_{13} C_{4}$ $715$ $_{14} P_{2}$ $182$ $_{13} C_{3}$ $286$ $_{12} P_{3}$ $1320$ $_{12} C_{2}$ $66$ $_{13} P_{4}$ $17160$ $_{12} C_{3}$ $220$ $_{12} P_{2}$ $132$ $_{14} C_{2}$ $91$ $_{14} P_{3}$ $2184$ $_{14} C_{4}$ $1001$ $_{12} P_{4}$ $11880$ $_{13} C_{2}$ $78$ $_{14} P_{4}$ $24024$ $_{14} C_{3}$ $364$ $_{13} P_{3}$ $1716$ $_{12} C_{4}$ $495$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Permutations and CombinationsAnswer keyVersion 1

Date Period

Evaluate each expression.

$_{13} P_{2}$ $156$
$_{13} C_{4}$ $715$
$_{14} P_{2}$ $182$
$_{13} C_{3}$ $286$
$_{12} P_{3}$ $1320$
$_{12} C_{2}$ $66$
$_{13} P_{4}$ $17160$
$_{12} C_{3}$ $220$
$_{12} P_{2}$ $132$
$_{14} C_{2}$ $91$
$_{14} P_{3}$ $2184$
$_{14} C_{4}$ $1001$
$_{12} P_{4}$ $11880$
$_{13} C_{2}$ $78$
$_{14} P_{4}$ $24024$
$_{14} C_{3}$ $364$
$_{13} P_{3}$ $1716$
$_{12} C_{4}$ $495$

How to do these

$_{8} P_{3}$

Eight choices, then seven, then six.
8 × 7 × 6.

The answer is $336$ .

Where students go wrong

Using permutations when order does not matter. Picking three people for a committee is a combination; picking first, second and third place is a permutation. If swapping two of your choices gives the same outcome, divide.

Also called nPr and nCr or the counting principle.

What you can put on this worksheet

Permutations: $_{8} P_{3}$ → $336$
Combinations: $_{8} C_{3}$ → $56$

Questions about these worksheets

Yes. Every permutations and combinations sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Geometry is usually taken around 9th or 10th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the permutations and combinations questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 2: permutations and combinations. Tick as many as you want and set how many of each, or let it spread them evenly.

Geometry permutations and combinations worksheet

Select your difficulty

Permutations and Combinations

Permutations and CombinationsAnswer keyVersion 1

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these permutations and combinations worksheets free?+

Do the permutations and combinations worksheets come with an answer key?+

Are these permutations and combinations worksheets printable?+

What grade are these permutations and combinations worksheets for?+

Can I get a different version of the same permutations and combinations worksheet?+

Is this a free alternative to Kuta Software for permutations and combinations?+

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What do students get wrong with permutations and combinations?+