GCSE Mathematics Question Analysis Topic: Mathematics - Permutation
Exam Question: In how many ways can you arrange 26 letters?
Consider 26 boxes, side by side. There can only be one letter in a box at a time. Therefore, the quantity of ways we may arrange 26 letters is equal to the quantity of ways we can fill the boxes with various letters. Any one letter from the total of 26 letters can go in the first box. Therefore, there will be 26 different ways to fill the first box. Consequently, 25 different ways will be possible to fill the second box, and so on.
As such, we can conclude that 26 letters can be arranged in 26! different ways, i.e. 26 x 25 x 24 ... x 1.
End of analysis. Great!