Tom’s dad built a 9 board-long fence, which Tom’s mother painted white. Tom, who has 3 different cans of paint – red, green and blue – would like to decorate the fence.
a) If he paints every second board (boards 2, 4, ...), in how many ways can he do it?
b) If he paints every second board, and if exactly one of the boards should be red, in how many ways can he do it?
c) If he paints every board, if exactly three boards should be red, and if the fence should be symmetrical, in how many ways can he do it?