Question

evelyn is reading about windemere castle in scotland. many years ago, when prisoners were held in various cells in the dungeon area, they began to dig passages connecting each cell to each of the other cells in the dungeon. if there were 20 cells in all, what is the fewest number of passages that had to be tunneled out over the years?

Explanation:

Step1: Use combination formula

The number of ways to choose 2 cells out of \(n\) cells (to dig a passage between them) is given by the combination formula \(C(n,2)=\frac{n!}{2!(n - 2)!}=\frac{n(n - 1)}{2}\). Here \(n = 20\).

Step2: Substitute \(n = 20\) into the formula

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Answer:

\(190\)