To find how many arrangements contain the two C's next to each other, I considered them as a unit and got 6!/3!=720/6=120.

I actually wrote them out and counted them to verify.

To find out how many arrangements containing the two C's also contain two or more S's next to each other, I considered each pair as a unit and got 5!=120.

Obviously, this isn't correct. in my actual count I only found 96.

What is the correct way to find the answer?

Thanks.