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 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:

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:

 green

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

This is the Viner family.

Here you have got:

The artist could have done

now find all the other ways:

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:

Work out some of the other ways they could sit.

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

1

2

  120

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).

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

The Tyers family

The Capel family

The Gunpowder Plot