Mai and books, againDiscrete Mathematics Level 3
After couple of days' break, Mai decided to continue with organising her home library. That means she will be doing the second bookshelf today (first one was done in the previous problem). Now, she has \( 9 \) books. Genres are mystery, thriller and romance, and from each genre, there are \( 3 \) books, one red, one blue and one green (for each genre). For today's arrangement, Mai wants to keep every genre together (she doesn't want to separate books with same genre) and also she doesn't want same-coloured books to be neighbouring. On how many ways can Mai organise the second shelf? Now, Mai knows the answer and she decided to help you (to some extent), so she offered a few answers. Only one is right.
Important: Like in the previous problem, two symmetrical arrangements are considered as \( 1 \) (123456789 is as same as 987654321).
To sum up: