How many words can be formed from the letters of the word 'computer' if each letter is to be used once?

1 Answer
Alan P.
Dec 6, 2015

#8! = 40320# (assuming any sequence of the #8# given letters is considered a "word")

Explanation:

There are 8 distinct letters in "computer#

In forming a "word"
#color(white)("XXX")#There are #8# choices for the first letter.
For each choice of a first letter
#color(white)("XXX")#there are #7# choices for the second letter.
For each choice combination of a first and second letter
#color(white)("XXX")#there are #6# choices for the third letter.
...and so on, resulting in
#color(white)("XXX")8xx7xx6xx...xx2xx1 = 8!# ways of selecting the letter order.

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