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In how many ways can the letters of the word "PROBLEM" be rearranged to make 7 letter words such that none of the letters repeat?

Correct Answer: 7!

Explanation:

There are seven positions to be filled.


 


The first position can be filled using any of the 7 letters contained in PROBLEM.


 


The second position can be filled by the remaining 6 letters as the letters should not repeat.


 


The third position can be filled by the remaining 5 letters only and so on.


 


Therefore, the total number of ways of rearranging the 7 letter word = 7*6*5*4*3*2*1 = 7! ways.


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