How many different words can be created using all the letters of the word QUESTION

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If you are strictly looking for the number of ways the letters can be arranged, then this question has already been answered.  However, not all 40,320 arrangements of the letters q-u-e-s-t-i-o-n will make a legitimate word.  

After some online research, I found that there are 161 words that can...

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If you are strictly looking for the number of ways the letters can be arranged, then this question has already been answered.  However, not all 40,320 arrangements of the letters q-u-e-s-t-i-o-n will make a legitimate word.  

After some online research, I found that there are 161 words that can be formed from these letters.

Approved by eNotes Editorial Team
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The letters of the word QUESTION have to be rearranged to create new words. Notice that all the letters of the word are unique.

There are 8 letters that make up the word QUESTION.

The number of permutations of n objects if r are selected is given by `P(n,r) = (n!)/((n-r)!)`

Here, n = 8 and r = 8

P(8,8) = `(8!)/(0!)` = 40320

There are 40320 different words that can be created using the letters of the word QUESTION.

Approved by eNotes Editorial Team