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We can write out 3! (three factorial) as 3x2x1, and we can write out 5! as 5x4x3x2x1.
This means that, since 3x2x1 is on the top and the bottom of the fraction, it cancels out.
This leaves ...

Let's think of the three boxes as A, B and C.
Say we choose box A.
There is a 1 in 3 chance that our box has the prize inside, and so a 2 in 3 chance that it does not.
When a box is o...

The average we're all familiar with is called the mean average - "add them all together and divide by how many there are", but sometimes another type of average makes more sense.As an example, c...