There are five bowls numbered $1$ to $5$. There are $5$ green balls and $6$ black balls. Each bowl is to be filled by either a green or black ball and no two adjacent bowls can be filled by green balls. If the same color balls are indistinguishable, then the number of different possible arrangements is
A. $8$ B. $7$ C. $13$ D. $256$
It is from a book for preparation of an exam in India.
As there are enough ball for all bowls, just check your options when starting to fill bowls. If 1 is green, 2 is black; need to fill 4 more according to the rules. If 1 if black, there are 5 more to fill. You see that from the number of solutions to 0 and 1 bowls you can compute how many there are for 3; from 2 and 3 you get 4, ...