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?

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

From INR

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 = 3^{5}

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