Lining up time

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CANVAS & STRETCHER

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

or

woman | man


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

but he could have done:

brown | green | red

red | brown | green



Find the other ways he could have done it:

green

   
       
       
       
       
       


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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?


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



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

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Extension


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

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.



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

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


For 7 look at the Capel family.



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

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.


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Fill in this chart using the information you already have:

1 person can be arranged

1

way
2 people can be arranged in

2

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

120

ways

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).

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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   ways

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?