easy Probability
A release-checked easy problem for training Combinations and Permutations, Combinatorics.
A teacher lines up $2n$ students of distinct heights in the following fashion: The two tallest students are placed in the $2$ center positions, and the heights of $n-1$ students to the left and $n-1$ students to the right of the two center students decrease outwards. How many arrangements of students are possible when $n = 5$?
This Probability problem is tagged Combinations and Permutations, Combinatorics. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.
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