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January 2008 - Question 2

As the three letters have to be different, this would be a permutation (as the order matters).
To work this out, we need to think 'How many choices do I have for the first letter?" "How many do I then have for the second letter?" and so on.
We can put A, C, T or G in the first position, so we have 4 choices. Let's choose A.
We can put C, T or G in the second position - 3 choices. Let's choose C.
We can put T or G in the third position - 2 choices. Let's choose T.
So we're going to multiply the number of choices together. 4 × 3 × 2 = 24 permutations.

You could also put this in your calculator as ⁴P₃.

If the letters can be repeated, all we need to do is square the number of letters we have originally (4) by the number of letters we need to restrict them to - 3.

4³ = 64.