GMAT Quant Questions | Permutation Q8

Reordering of distinct elements | Reordering Letters of a Word

This GMAT quant practice question is a classic permutation question. Concept tested: Reordering 'n' distinct elements. A GMAT 600 level, easy problem solving sample question.

Question 8: 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

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Explanatory Answer | GMAT Reordering of Distinct Elements

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.

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