White Dot, Black Dot

Probability Level 4

The diagram below shows a $2 \times 10$ grid of dots (of negligible size) that alternate between black and white. How many ways are there to draw ten line segments between the dots such that

each white dot is connected to exactly one black dot (and vice versa),
no segment passes through more than two dots, and
none of the segments intersect each other?

Bonus: Generalize for drawing $n$ segments on a $2 \times n$ grid, where $n$ is a positive integer.