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

2 Answers
Pop Quiz Whiz · Monzur R.
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)!)#

EZ as pi · Monzur R.
Aug 18, 2017

#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#

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