at first level,there can be only 1..hence only 1 way
at second level,there can be 2 or 3 ,hence 2 ways
at third level,there can be 4,or 5 or 6 or 7 ,hence 4! ways
at fourth level,there can be 8 or 9or 10 or 11 or 12 or 13 or 14 or 15 ,hence 8! ways
so,total number of min heaps are 1*2* 4! * 8! ways . It looks like this ....
But actually, question only asks to handle leaf nodes not internal nodes, hence the numbers 2,3,4,5,6,7 can be arranged any way.
At root, 1 is for sure fixed, but for 2,3,4,5,6,7 , total ways will be
$C(6,3) * 2! * 1 * 2! * 8! = 3225600 $ ways.
PS: $C(6,3)$ :- Choose any three elements for left $3$ positions and arrange them in $2!$ ways.
Then, right $3$ positions can be permuted in $2!$ ways .