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

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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.

chadbutler's profile pic

chadbutler | High School Teacher | (Level 1) Adjunct Educator

Posted on

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.

Sources:

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