Can somebody help me prove that there are 26! different ways to arrange the letters in the alphabet?
$\displaystyle 26 \times 25 \times 24 \times ... \times 2 \times 1 = 26! $
There are 26 possibilities for the selection of the first letter, and for each of these 26 possibilities there are 25 possibilities for the second letter, then 24 possibilities for the third, and so on in an expanding tree of possibilities.
Sorry to say this is almost a nonsense question.
It is equivalent to saying that ‘ABCD’ can be arranged in $\displaystyle 4!$ ways.
Well there are four ways to have a first term.
There are three ways to have a second term.
There are two ways to have a third term.
There is one way to have a fourth term.