1) In the diagram below, we want to color two of the dots red, two of the dots green, and two of the dots blue, so that each pair of dots of the same color is joined by an edge. How many ways are there to color the dots?
2) The below grid contains 6 rows, 6 columns, and 6 outlined boxes. One of the 6 * 6=36 small squares in this grid has been shaded.
In how many ways can 5 of the other 35 small squares in this grid be shaded so that exactly one square in each row, column, and outlined box is shaded?