The GMAT Sample Math question for the day is from the topic Permutation and Combination on rearranging letters of a word.
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?
- None of these
The correct choice is (A) and the correct answer is 7!
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.
eBooks on Permutation Combination & Probability