Let's take scenarios to help us.
Since, she must use 3 colours, then at least 3 pieces on the grid are of different colours. So, the remaining three will be of focus for this question. Another restraint we need to consider is that we must have more blue than red or pink.
Scenarios:
3 blue - 1 pink - 2 red (2 ways, because the pink and red can swap)
4 blue - 1 pink - 1 red
Hence, there are only three ways.