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Grade 10 Challenge: Counting & Arrangements Worksheet with Answers

Grade 10 (US) · Year 11 (UK) · Class 10 (India) · Math

Unit 8: Going FurtherChallenge PuzzlesChallenge

Counting outfits, handshakes, arrangements and grid paths — an introduction to combinatorics. This free high 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 10 · 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 3 shirts, 5 pairs of pants and 3 hats. How many different outfits of one shirt, one pair of pants and one hat can you make?

Answer: 45

1
How many 3-digit numbers can be made from the digits 1 to 5 if no digit is repeated?
Show your work
Answer
2
How many 3-digit numbers can be made from the digits 1 to 4 if no digit is repeated?
Show your work
Answer
3
How many 3-digit numbers can be made from the digits 1 to 6 if no digit is repeated?
Show your work
Answer
4
On a grid, you walk from the bottom-left corner to a point 3 blocks right and 2 blocks up, moving only right or up. How many different shortest paths are there?
Show your work
Answer
5
On a grid, you walk from the bottom-left corner to a point 2 blocks right and 4 blocks up, moving only right or up. How many different shortest paths are there?
Show your work
Answer
6
You have 3 shirts, 4 pairs of pants and 4 hats. How many different outfits of one shirt, one pair of pants and one hat can you make?
Show your work
Answer
7
At a meeting, 10 people each shake hands once with everyone else. How many handshakes take place?
Show your work
Answer
8
How many different ways can the letters of the word FROG be arranged? (all letters are different)
Show your work
Answer
9
How many different ways can the letters of the word CLIMB be arranged? (all letters are different)
Show your work
Answer
10
How many ways can a team of 2 be chosen from 7 students?
Answer
11
How many ways can a team of 2 be chosen from 10 students?
Answer
12
How many ways can a team of 3 be chosen from 7 students?
Answer

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Teacher's comments

Free printable worksheets with answer keys · aethelsystems.com/worksheets/math/10/challenge_counting

Answer key (click to show)

1.60
2.24
3.120
4.10
5.15
6.48
7.45
8.24
9.120
10.21
11.45
12.35

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