$Counting: permutations and combinations: stretch: math worksheet for Grade 10, page 1 preview$

Math worksheet · Mathematics

Counting: permutations and combinations: stretch · Grade 10

Count arrangements and selections. 16 problems at a stretch level for Grade 10, with an answer key for grown-ups.

Grade 10 · ages 15 to 16
Hard
25 to 35 minutes
2 pages
Free

The answer key is a separate page for grown-ups. Sign in to download it.

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The 16 problems on the sheet

Directions: Work out each count.

1. Ways to choose 4 of 12 books:
2. Ways to line up 2 of 4 runners in order:
3. 7 friends in a row, all orders:
4. Ways to choose 2 of 4 books:
5. Ways to line up 2 of 9 runners in order:
6. Ways to choose 4 of 6 books:
7. Ways to line up 4 of 10 runners in order:
8. Ways to line up 3 of 12 runners in order:
9. 4 friends in a row, all orders:
10. Ways to choose 3 of 5 books:
11. Ways to line up 3 of 10 runners in order:
12. Ways to choose 3 of 11 books:
13. Ways to line up 3 of 11 runners in order:
14. Ways to choose 3 of 8 books:
15. 5 friends in a row, all orders:
16. Ways to choose 2 of 11 books:

What your child practices

Your child practices math for Grade 10 with this math worksheet.

Grades and ages: Grade 10, ages 15 to 16
Time: About 25 to 35 minutes
Subject: Mathematics
Level: Hard for Grade 10
Answer key: Yes, for grown-ups who sign in
Printing: 2 pages, US Letter or A4, low-ink option
Updated: October 15, 2026

How to use it

Try the first question together so the format is clear. Then let your child work through the rest, showing their thinking on the page. It is one of the harder sheets for Grade 10, best once the basics of the topic are secure. Its 2 pages split well across two sittings.

An answer key comes with it as a separate page that grown-ups download after signing in.

Tip for grown-ups: Check the first three problems together before your child carries on alone; most mix-ups show early.

Done on paper? A grown-up can record it on the child's page in PlayOwl; downloading alone doesn't count as finished.