Your answer to the first one is correct. Your answer to the second did incorrect though. After the first group has been formed, there are 6 people left to form a group out of, so the answer is $6C4$.
Your answer to the first one is correct. Your answer to the second did incorrect though. After the first group has been formed, there are 6 people left to form a group out of, so the answer is $6C4$.