with 3 as root we can insert in 8 different combinations of avls as {3} {2,6}{1,5,7}{4} ;
{3}{1,6}{2,5,7}{4};
{3}{2,5}{1,4,6}{7} ;
{3}{1,5}{2,4,6}{7};
{3}{2,6}{1,4,7}{5};
{3}{1,6}{2,4,7}{5};
{3}{2,5}{1,4,7}{6};
{3}{1,5}{2,4,7}{6};
where each of the combination permute in 2!*3! =12 ways
this gives total of 12*8 i.e. 96 insertion sequences with 3 as root
with 4 as root, balanced avl only kind of AVL is created and sequences is {4}{2,6}{1,3,5,7} which gives 48 permutations
with 5 as root we have 8 insertion sequence with 12 permutations in each {same as 3 as root} i.e. total of 12*8 i.e 96 sequence.
So total ways to insert keys in AVL without rotation is 48+2*96 i.e 48+ 192 i.e. 240..................