This GMAT quant practice question is a classic permutation question. Concept tested: Reordering 'n' distinct elements.

#### Question: 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?

- 7!
^{7}C_{7}- 7
^{7} - 49
- None of these

#### Video Explanation

Scroll for explanatory answer text#### Explanatory Answer

##### 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.

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