Mai and books, again
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 books. Genres are mystery , thriller and romance , and from each genre, there are 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 (123456789 is as same as 987654321).
To sum up:
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1 solution
Solution:
On first place, she can put any book (9 choices). On the second and the third place, she can only put books whose genre is as same as the first book's genre (2nd place: 2 choices, 3rd place: 1 choice). On the 4th place, she can place any of the left books, but it has to be different-coloured from the 3rd book (4 choices). Now, the genre is established, and 5th and 6th place is meant for the same genre as the 4th place (5th: 2 choices 6th: 1 choice). The last three places are meant for the last genre. The 7th book has to be different-coloured from the 6th one (2 choices, 8th book: 2 choices, 9th book: 1 choice).
That is 9 × 4 × 2 4 . Because of the important condition, this is divided by two. So the answer is 9 × 4 × 2 3 = 2 8 8 .