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A Maths Starter of The Day

How many different ways can four people stand in line?

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Keywords: 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 06, 2009
  • "Most of the class liked this. Thank you."
  • Amal, London
  • Wednesday, December 02, 2009
  • "There are 24 ways."

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This starter has scored a mean of 3.7 out of 5 based on 59 votes.
 

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Answer

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

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?