This GMAT quant practice question is a classic permutation question. Concept tested: Reordering 'n' distinct elements.
- None of these
Number of ways of rearranging 'n' distinct objects
The letters of the word PROBLEM are distinct.
There are seven positions to be filled to form 7 letter words using the letters in the word PROBLEM.
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 and so on.
Therefore, the total number of ways of forming 7 letter words = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 7! ways.
Choice A is the correct answer.
Key Takeaway: 'n' distinct objects can be reordered in n! (factorial n) ways.