Bus Stop

Standing In Line

How many different ways can four people stand in line?

Note for Teacher: Click and drag the characters above to help explain the task.

Person1 Person2 Person3 Person4

A Mathematics Lesson Starter Of The Day

Topics: Starter | Combinations | Investigations | Probability

  • Malcolm, Dorset
  • They enjoyed this one!

    On the extension, there are two errors not one!
  • Year 8 set 1, Freebrough Specialist Engineering College, Cleveland
  • Actually, there is not one, or two mistakes in the extension question. There are in fact three mistakes!
  • Miss Chavda, KSHS, Lincolnshire
  • Year 7s enjoyed this, and found a logical way to find all the solutions - 7A
  • Helsby High School, 9y4
  • Most of the class liked this. Thank you.
  • Amal, London
  • There are 24 ways.
  • N Cox, Ipswich
  • Great starter. Extended to four 5, 6 and 7 people and to the use of the factorial key on the calculator.
  • Angel, Sacred Heart High
  • There are 24 ways to stand in the straight line!
  • James, Weston
  • I really enjoyed this starter, because our class stood up and lined up for us to work out the answer :).
  • Mr Musker And Class 4, Warden Hill Junior School
  • We think that there are 24.
  • Year 8 Legends, King James's
  • We found 24 too. We also enjoyed doing the line-up.
  • Year 6 - Sir John Heron School, Newham
  • Nice starter. The children in y6 need another one to consolidate!
  • Mr Kavanagh's Fifth Class, Cork, Ireland
  • We figured out that if there were ten people in the line there would be 3,628,800 different ways to arrange them.
  • Transum,
  • Many people have said how much they enjoyed this activity. If you would like to move on to something related and something which the pupils can do on their computers, slates or iPads etc then try the Combinations and Permutations list of activities such as Ice Cream Combinations, Misfits and Striped Sweets. It will reinforce the idea of having a logical, well-ordered strategy for listing all the possibilities.
  • Mrs. Lorenzo,
  • This was an awesome problem to solve. My class roared with laughter at the sight of the characters - they add a fun dimension to the puzzle. Ashika got it right away. My grade 3 class did it. I was suprised at what the're capable of!

How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.
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Online Maths Shop

Laptops In Lessons

Teacher, do your students have access to computers such as tablets, iPads or Laptops?  This page was really designed for projection on a whiteboard but if you really want the students to have access to it here is a concise URL for a version of this page without the comments:


However it would be better to assign one of the student interactive activities below.

Laptops In Lessons

Here is the URL which will take them to the Systematic Listing activity.


Student Activity

Extension activities

Here is a solution to this problem with at least one mistake.
Can you spot the mistake(s)?

In how many ways can 5, 10 or 100 people stand in line?

In how many different ways can the letters in the word Transum be arranged?

In how many different ways can the letters in the word Google be arranged?

Curriculum Reference

See the National Curriculum page for links to related online activities and resources.


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