Alberto has in front of him 13 cells arranged one above the other, and wants to insert the numbers from 1 to 10, one per cell (three cells will remain empty). He also wants that, if two numbers are written in cells that touch each other, the one higher up is greater. In how many ways can he do this?
Pick one
Solution
The answer is (D). The four cells left blank partition the 10 numbers into four subsets (possibly empty). Within each of these subsets, the order of the numbers inserted into the cells is determined. Since each of the 10 numbers can end up in any of the four sets, the set of possible arrangements is .
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