approach for FATCHEF correct or not?

lets say there are paint buckets at i and jth positions,so the number of possible colorings between i and j (ith and jth planks will have fixed colors cos the brush acquires the paint buckt color )if i and j are different the number of possibilities are j-i else 1,

for example
1 2 3 4 5 6 and buckets and 3 and 5 (left to the left extreme and right to the right extreme will have only 1 color) so 1*(5-3)*1=2 there are only 2 possibilities Is this approach correct?

Yes, its correct! Just remember that the order of positions will not be sorted , thus you first need to sort the bucket positions , then apply this logic.