GMAT Permutation Combination Question 6

This GMAT quant practice question is a GMAT 600 to 650 level problem solving sample question. Concept covered: Sampling with Replacement question in Permutation and Combination.

Question 6: 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

Explanatory Answer | GMAT Sampling with Replacements Q6

Sampling with Replacement

The first letter can be posted in any of the 3 post boxes. Therefore, we have 3 possibilities for the first letter.
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 in which the 5 letters can be posted in 3 boxes is 3 × 3 × 3 × 3 × 3 = 3⁵

Choice D is the correct answer.