# How many four letter words are possible using the first 5 letters of the alphabet if letters can not be repeated?

Aug 18, 2017

If 'word' means any 4 letters in a given order, then it is 120.

#### Explanation:

Using the permutation function, we can see how many way there are to pick 4 things in a specific order out of 5 things. I'm not going to derive the formula here, but:

""^nP_r= (n!)/((n-r)!)

Aug 18, 2017

$5 \times 4 \times 3 \times 2 = 120$ different 'words'

#### Explanation:

You can work out the number of possible 'words' by considering the number of choices available for each letter.

There are $5$ choices for the first letter: $a , e , i , o , u$

Number of options = $5$

Once the first letter is chosen, there will be $4$ letters to choose.

Number of options $= 5 \times 4 = 20$

Once the second letter is chosen, there will be $3$ letter to choose.

Number of options $= 5 \times 4 \times 3 = 60$

Once 3 letters are chosen there are $2$ letters to choose from:

Number of options $= 5 \times 4 \times 3 \times 2 = 120$