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The question given below is a sample question in Couting Methods and Permutation Combination. This particular question is a case of sampling with replacement and with ordering.

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?
A. ⁵C₃
B. ⁵P₃
C. 5³
D. 3⁵
E. 15

Correct answer is 3⁵. Choice D.

Explanatory Answer

A question of this kind is a typical example for sampling with replacement.

The first letter can be posted in any of the 3 post boxes. Therefore, it has 3 choices.

The question explicitly states that any number of letters can be posted in all of the three boxes.

Hence, the second, the third, the fourth and the fifth letter can each be posted in any of the 3 post 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 choice.

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