Lining up time

Page 1


Lining up time: how many ways can you arrange the people in a portrait?
Quite a few portraits show several people standing or sitting in a line. You are going to work out how many different ways this could be done - and think why the artist actually chose the particular arrangement that you see in some of the pictures.

David and Eva Maria Garrick
David Garrick and Eva Maria Garrick
by Sir Joshua Reynolds, oil on canvas, exhibited 1773

Here is the portrait of David Garrick and his wife Eva Maria.

The artist only has 2 ways to arrange them:

man woman

woman man

Reynolds, Chambers and Wilton
Sir Joshua Reynolds, Sir William Chambers and Joseph Wilton
by John Francis Rigaud, oil on canvas, 1782

  Now look at this picture with 3 men, each wearing a different coloured coat. The artist has shown them like this:

green red brown

but he could have done:

brown green red
red brown green

Find the other ways he could have done it:







Page 2

How many different ways are there to arrange 3 people?




Do you think one man looks more important than the other two or do all three look about equal?



Vyner Family
The Family of Sir Robert Viner
by John Michael Wright, oil on canvas, 1673

This is the Viner family.

Here you have got:

girl mother boy father

The artist could have done

father girl mother boy

now find all the other ways:



How many different ways are there to arrange 4 people?




Charles is the smallest person in the picture. Where has the artist put him to make him look important? What else has the artist done to help you notice him?




Page 3

Five Children of Charles I
Five Children of Charles I
by Unknown artist after Sir Anthony Van Dyck, oil on canvas, (1637)

These are the children of King Charles I. Their names are:

Mary James Charles Elizabeth Anne


Work out some of the other ways they could sit.








Now guess how many different ways they could sit (don't try to work out all of them).

  I guess   different   ways

Why did the artist choose Charles to be in the middle, do you think?






Page 4



  Jonathan Tyers and his family
Jonathan Tyers and his family
by Francis Hayman, oil on canvas, 1740

You are now going to look at some portraits with more people in. Don't try to count all the different ways to arrange them as there are hundreds of ways!

For 6 look at the Tyers family.

  Capel Family
The Capel Family
by Cornelius Johnson (or Jonson), oil on canvas, circa 1640

  For 7 look at the Capel family.

  The Gunpowder Plot Conspirators
The Gunpowder Plot Conspirators, 1605
by Unknown artist, engraving, circa 1605

For 8 look at Guy Fawkes and the Gunpowder Plot conspirators.

There is a way to work out how many ways to arrange a set number of people.



Page 5

Fill in this chart using the information you already have:


1 person can be arranged


2 people can be arranged in


3 people can be arranged in    ways
4 people can be arranged in    ways
5 people can be arranged in



How good was your guess for 5 people?





Can you find a pattern which links the number of people with the number of ways they can be arranged?

(CLUE - it's to do with multiplying, and you always use your last answer in the next sum).







Page 6

The pattern you have found is called the factorial for each number and is written !2.

So !5 means 1 x 2 x 3 x 4 x 5 = 120

Now use a calculator (if you need one) and work out the answers for those other portraits

  Tyers Family

The Tyers family

Capel Family

The Capel family

  Gunpowder Plot Conspirators

The Gunpowder Plot

The Tyers family, 6 people, can be arranged in    ways
The Capel family, 7 people, can be arranged in    ways
The 8 Gunpowder Plot conspirators can be arranged in



If you arranged all the people in your class in a line, how many different ways could you do it? - you will need a calculator for this!




Now make a portrait of a group of people in your class - how will you arrange them?