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?

^{5}C_{3}^{5}P_{3}- 5
^{3} - 3
^{5} - 2
^{5}

#### Video Explanation

Scroll for explanatory answer text#### 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 = 3^{5}

Choice D is the correct answer.

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