GMAT® Permutation Practice

Concept: Sampling with replacement

This GMAT math practice question is a sampling with replacement question in Permutation and Combination.

Question: In how many ways can 5 letters be posted in 3 post boxes, if any number of letters can be posted in all of the three post boxes?

  1. 5C3
  2. 5P3
  3. 53
  4. 35
  5. 25

Video Explanation

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Explanatory Answer

Sampling with replacement

The first letter can be posted in any of the 3 post boxes. Therefore, we have 3 possibilities.

Similarly, the second, the third, the fourth and the fifth letter can each be posted in any of the 3 post boxes.
Each of the 5 letters has 3 possibilities because we can post any number of letters in all of the boxes.

Therefore, the total number of ways the 5 letters can be posted in 3 boxes is 3 * 3 * 3 * 3 * 3 = 35

Choice D is the correct answer.

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