For these types of combinatorics problems, it is good to think about real life scenarios to help interpret the problems.

Here the key wording is "in succession" meaning that there is a first bath and then a second bath, implying that the order does matter.

(Of course part (a) and part (b) can be done independently, but also thinking of the question in part (b) can help reinforce the intended interpretation in part (a), as in part (b) it is saying that there is an order that can matter in some cases.)