Bus Stop

A Mathematics Lesson Starter of the Day

Standing In Line

How many different ways can four people stand in line?

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Topics: Starter | Investigations | Probability

  • Malcolm, Dorset
  • Monday, March 12, 2007
  • "They enjoyed this one!

    On the extension, there are two errors not one!"
  • Year 8 set 1, Freebrough Specialist Engineering College, Cleveland
  • Thursday, November 15, 2007
  • "Actually, there is not one, or two mistakes in the extension question. There are in fact three mistakes!"
  • Miss Chavda, KSHS, Lincolnshire
  • Wednesday, March 12, 2008
  • "Year 7s enjoyed this, and found a logical way to find all the solutions - 7A"
  • Helsby High School, 9y4
  • Tuesday, October 6, 2009
  • "Most of the class liked this. Thank you."
  • Amal, London
  • Wednesday, December 2, 2009
  • "There are 24 ways."
  • N Cox, Ipswich
  • Tuesday, March 16, 2010
  • "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
  • Saturday, March 5, 2011
  • "There are 24 ways to stand in the straight line!"
  • James, Weston
  • Friday, March 11, 2011
  • "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
  • Tuesday, March 15, 2011
  • "We think that there are 24."
  • Year 8 Legends, King James's
  • Monday, March 19, 2012
  • "We found 24 too. We also enjoyed doing the line-up."
  • Year 6 - Sir John Heron School, Newham
  • Monday, March 11, 2013
  • "Nice starter. The children in y6 need another one to consolidate!"
  • Mr Kavanagh's Fifth Class, Cork, Ireland
  • Tuesday, March 12, 2013
  • "We figured out that if there were ten people in the line there would be 3,628,800 different ways to arrange them."

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This starter has scored a mean of 3.7 out of 5 based on 164 votes.


Previous Day | This starter is for 12 March | Next Day

 

Answers

There are 24 different ways in which 4 people can stand in line

There are four people who could be first in line. Once that person has been decided there are three people who could be second and so on.

The total is therefore 4 x 3 x 2 x 1

(Sometimes written as 4!)

=24


Laptops In Lessons

Teacher, do your students have access to computers?
Do they have Laptops in Lessons or iPads?

Whether your students each have a TabletPC, a Surface or a Mac, this activity lends itself to eLearning (Engaged Learning).

Laptops In Lessons

Here is the URL for a concise version of this page without comments or answers.

Transum.org/go/?Start=March12

Here is the URL which will take them to a probability activity.

Transum.org/go/?to=Great

 

 



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?



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