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If a coin is flipped twenty times, how many ways are there to get exactly ten tails and ten heads?

Suppose \(10\) points are drawn on a plane such that exactly \(4\) of the points are collinear and among the remaining points, no three points are collinear. How many distinct lines can be drawn by connecting any \(2\) among these \(10\) points?

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How many ways can the integers \(1,2,3,4,5,6\) be arranged such that \(2\) is adjacent to either 1 or 3?

**Details and assumptions**

2 could be next to both 1 and 3.

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