GMAT® Math Practice - Rearranging Letters

Concept: Reordering 'n' distinct elements.

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?

  1. 7!
  2. 7C7
  3. 77
  4. 49
  5. None of these

Explanatory Answer

Video explanation will be added soon
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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