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

Explanatory Answer

Video explanation will be added soon
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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