Probability Games Statistics In Your World 
Student Notes
Teachers Notes

Trains & Boats & Planes
You will need some coloured pencils. If you do not have any, you could use different shadings.
John has a picture of a boat with two sails.


Figure - 6 John's boat

He has three different colours. He wants to use all three colours, so he decides to use a different colour for each part.

a How many different ways can John colour the two sails?
b How many different ways can he colour the whole boat?
c Compare your answers with those of a friend.

John found a fourth different coloured pencil hidden in his case. 'So he can use any three of the four coloured pencils.

d How many ways can he now colour the two sails?
e How many different ways can he now colour the boat?

Lynn has a picture of a train, which has three carriages and an engine.


Figure 7 - Lynn's train

Lynn only has two coloured pencils. She will have to colour some parts, or even the whole train, the same colour.

f How many different ways can she colour the engine and first carriage?
g How many different ways can she colour the whole train?

Remember that each part can be shaded with only one colour.

h Compare your answers with those of a friend.

Make up some examples of your own, for example, aeroplanes, houses, flags. Start with four or fewer parts.

j Can you see any pattern in your results?

 

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