Question

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

Answer 1

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)!)`

Answer 2

`5xx4xx3xx2 = 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 xx 4 = 20`

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

Number of options `= 5 xx 4 xx 3= 60`

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

Number of options `= 5 xx 4 xx 3xx 2 = 120`