a) 24 different arrangements, 4! = 24
b) 12 arrangements start with a vowel.
a) In choosing the first letter, there are 4 options, but once one has been chosen, there are only 3 tiles remaining to choose from for the second letter. Similarly there is a choice of 2 letters for the third letter, but only one letter is left for the last position.
The total number of different arrangements is therefore:
4 x 3 x 2 x 1 = 24.
This is also called 4 factorial, denoted by 4!
b) The same approach can be used if the first letter is to be a vowel.
2 of the letters are vowels, A and E.
Therefore there is a choice of 2 letters for the first position, 3 for the second, 2 for the third and no choice for the fourth place.
The number of arrangements starting with a vowel is given by:
2x3x2x1 = 12.
One could also realise that as half of the letters available are vowels, half of the total number of arrangements would start with a vowel.