A bookshelf contains 3 spanish books, 5 chinese books, and 6 korean books. Each one is different from one another. How many arrangements can be made of these books if no two spanish books can be next to each other?

2184 ways to arrange the three Spanish books of which 78 ways would rsult in two spansh books side-by-side

so 2106 ways to arrange the Spanish books

then the other 11 slots can hold the other books in 11! = 39916800 ways

2106 * 39916800 = 84 064 780 800 ways (?)