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Betty's Window: Solution

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windowBetty has a window in her bedroom that looks like this. It has four panes of glass.

For her birthday she was given two big stickers with a ballet dancer on and two with horses. She wants to put a different sticker on each pane of glass. In how many ways can she do this?
 
Solution
 
There are 6 ways to arrange the stickers.
 
Here is how you can work it out:
 
First take one of the ballet dancer stickers. Try putting it in the top left pane. Then there are three places the other ballet dancer sticker could go. Have a look at the picture below.
three windows
 The horses go in the spare panes.
 
Now let’s try the first ballet dancer in the top right pane. We can’t put the second one in the top left pane because that would be the same as one we have done above. So there are only two places that she can go.
two windows.
 
Now try putting the first ballet dancer sticker in the bottom left position. As we can see there is now only one place the other one can go.
one window.
 
If we try to put the ballet dancer in the bottom right pane, the other sticker has to go in a position we have already shown.
 
So there are 3 + 2 + 1 possible ways of decorating Betty’s windows.
 
Extension
 
Suppose that Betty had a ballet sticker, a horse sticker, a cat sticker and a candy cane sticker. In how many different ways could Betty decorate her windows?