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Grade 8 Challenge: Counting & Arrangements Worksheet with Answers

Grade 8 (US) · Year 9 (UK) · Class 8 (India) · Math

Unit 7: Going FurtherChallenge PuzzlesChallenge

Counting outfits, handshakes, arrangements and grid paths — an introduction to combinatorics. This free middle school worksheet has 12 questions and a full answer key. Print it or save it as a PDF — every answer is checked by code, not guessed.

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Challenge: Counting & Arrangements

Grade 8 · Math

Score___ / 12

Name

Class

Date

Learning goal: Challenge Puzzles

Directions: Solve each problem. Show your work, then write your answer in the box.

Example

You have 2 shirts, 4 pairs of pants and 1 hats. How many different outfits of one shirt, one pair of pants and one hat can you make?

Answer: 8

  1. 1

    At a meeting, 9 people each shake hands once with everyone else. How many handshakes take place?

    Show your work
    Answer
  2. 2

    How many ways can a team of 3 be chosen from 7 students?

    Answer
  3. 3

    On a grid, you walk from the bottom-left corner to a point 2 blocks right and 2 blocks up, moving only right or up. How many different shortest paths are there?

    Show your work
    Answer
  4. 4

    How many ways can a team of 2 be chosen from 9 students?

    Answer
  5. 5

    How many ways can a team of 3 be chosen from 5 students?

    Answer
  6. 6

    At a meeting, 11 people each shake hands once with everyone else. How many handshakes take place?

    Show your work
    Answer
  7. 7

    At a meeting, 13 people each shake hands once with everyone else. How many handshakes take place?

    Show your work
    Answer
  8. 8

    You have 5 shirts, 4 pairs of pants and 2 hats. How many different outfits of one shirt, one pair of pants and one hat can you make?

    Show your work
    Answer
  9. 9

    You have 4 shirts, 2 pairs of pants and 2 hats. How many different outfits of one shirt, one pair of pants and one hat can you make?

    Show your work
    Answer
  10. 10

    How many 3-digit numbers can be made from the digits 1 to 7 if no digit is repeated?

    Show your work
    Answer
  11. 11

    How many 3-digit numbers can be made from the digits 1 to 6 if no digit is repeated?

    Show your work
    Answer
  12. 12

    You have 5 shirts, 4 pairs of pants and 3 hats. How many different outfits of one shirt, one pair of pants and one hat can you make?

    Show your work
    Answer

How did I do?

Teacher's comments

Free printable worksheets with answer keys · aethelsystems.com/worksheets/math/8/challenge_counting

Answer key (click to show)
  1. 1.36
  2. 2.35
  3. 3.6
  4. 4.36
  5. 5.10
  6. 6.55
  7. 7.78
  8. 8.40
  9. 9.16
  10. 10.210
  11. 11.120
  12. 12.60

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How to use this worksheet

  • Works well as a bell-ringer, exit ticket, homework set or quick quiz.
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Challenge: Counting & Arrangements at other grades

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Guides for teaching Challenge: Counting & Arrangements

What Are the Common Core and NGSS Standards? A Parent's GuideWhat learning standards are, how to read a code like 3.NF.A.1 or MS-PS1-2, what each grade covers in Math, English and Science, and how to use them at home.

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Does this Grade 8 Challenge: Counting & Arrangements worksheet come with answers?

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