Cars can be lined up in traffic jams in different ways.

For example two cars could be ordered;

red car, blue car *or *blue car, red car.

How many ways can three cars be lined up?

How many ways can four cars be lined up?

[See also Combinations and Permutations]

Investigate further.....

Do you have any starting
points for mathematical investigations or comments about the investigations we have presented here?

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ideas.

A mathematical investigation is quite different to other mathematical activities.
The best investigations are open ended and allow students to choose the way they
work and how they record their findings. It is one of the few occasions when
'going off on a tangent' is not only acceptable but actively encouraged (within
reason).

Students may ask for 'the answers' but this supposes that the activity is
closed. Investigations can always be extended by varying the initial
instructions or asking the question 'what if...?'. Sometimes students point out
that the instructions are ambiguous and can be interpreted in different ways.
This is fine and the students are encouraged to explain how they interpreted the
instructions in their report.

Some students may benefit from a writing frame when producing the reports
of their investigations. Teachers may suggest sections or headings such as
Introduction, Interpretation, Research, Working and Conclusion or something
similar.