Tiffany uses $3$ identical red gems, $6$ identical blue gems, and $9$ identical pearls to make a necklace. If any two gems cannot be adjacent, how many ways does she have to make the necklace? (After flipping or rotating, if two neckleces can be the same, then count them as $1$ way.) 
Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations
The $9$ pearls should be put in each of the two gems. Thus, just consider the combination of gems:  if all red gems are together, she has $1$ way;  if two red gems are together, she has $3$ ways;  if all the red gems are not together, the blue gems can be put $1-2-3$, $1-1-4$ or $2-2-2$, so there are $3$ ways.  There are $7$ ways. 