I managed to do this question the wrong way around.
I have 5 red and 4 blue beads.
oh dear, they are meant to be balls, never mind, mine are balls with holes to turn them into beads.
I have thought of it as a bangle so rotations are the same.
Plus the bangle can put on either way so that cuts down on possibilities as well.
At first I just thought of it as a standard permutation question but it became clear to me that standard 'simple' formula methods were not going to work.
So I resorted to drawing all the possibilities.
This is what I came up with.
If anyone says I have missed any, or that I have double-counted I am all ears.
Only one of these has all the blue separate.
So if you know anything at all about probability you can finish it yourself.