Deciding whether a given language is regular I am struggling with a homework assignment. This next question seems to be pretty easy, once I get what I feel like I'm missing now. Anyway, here goes:


  Decide if the following language is regular or not and prove your
  claim.
  
  $$L=\{a^{i_{1}}ba^{i_{2}}ba^{i_{3}}ba^{i_{4}}ba^{i_{5}}ba^{i_{6}}ba^{i_{7}}b|i_{1}&gt;i_{2}&gt;i_{3}&gt;i_{4}&gt;i_{5}&gt;i_{6}&gt;i_{7};i_{1}&lt;100\}$$


So, how do I go about doing so? Is there a thumb rule that might help? I was trying to use the pumping lemma to prove that it is not regular, but couldn't do it. I'm not even sure it really is not regular.

Any suggestions?
Hint: Consider how many words are in $L$. The answer will then be immediate.