maths question help please

hi, please could i have some help on part biii
I'm confused why it cannot be P(BBBW) and why it has to be p(bbwb)? in the first case, if you add a white, black will still be greater?
thanks!

hi, please could i have some help on part biii
I'm confused why it cannot be P(BBBW) and why it has to be p(bbwb)? in the first case, if you add a white, black will still be greater?
thanks!

Both probabilities refer to transferring all discs from A to B and you should be able to see that
P(BBB) = P(BBBWW)
and smilarly for
P(BBWB) = P(BBWBW)
There are no other combinations (on the right) that give the desired sequence for the 5 discs