# 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

## GMAT Live Online Classes

### 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.

#### GMAT Online CourseTry it free!

Register in 2 easy steps and
Start learning in 5 minutes!

#### GMAT Live Online Classes

Next Batch Aug 10, 2024

Work @ Wizako

##### How to reach Wizako?

Mobile: (91) 95000 48484
WhatsApp: WhatsApp Now
Email: learn@wizako.com