Adam has made a snowman. He has 4 hats and 3

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Adam has made a snowman.
He has 4 hats and 3 scarves.
He is going to put one hat and one scarf on the snowman.
How many different ways are there to dress the snowman?
How can you prove that you have found them all?
What if there were 5 hats or 4 scarves? Can you find a rule that is always true?
What if there was a selection of coats too?