Number of possible min heaps The number of possible min-heaps containing each value from {1, 2, 3,
  4, 5, 6, 7} exactly once is --------------


According to me, the answer should be 48. The first element 1 is fixed as root. The next level contains elements 2 and 3. The third level contains 4,5,6,7. 
Therefore, the total no. of cases should be 4! * 2!=48. 

But my solution manual says that the answer should be 80. 

Am I correct? If not, what am I doing wrong?

Thanks in advance
The second level can contain other numbers than 2 and 3. See for example

      1
     / \ 
    2   5
   / \     
  3   7     
 / \  
4   6


It is also unclear if you count isomorphic trees. See this question for a related answer.