10, 20, 40,50 and 90,80,70 will always come in this order since we have a binary search tree.
Ex. 10 20 40 50 90 80 70{S,S,S,S,L,L,L} or 10 90 20 40 80 70 50 {S,L,S,S,L,L,S}.
(S- no. Smaller than 60, L-no. Larger than 60)
So we have got 2 groups of 3 and 4 numbers each. Say, group 1={L,L,L} containing nos. >60, group 2={S,S,S,S} containing nos.<60. But group order remains same (10,20,40,50) and (90,80,70) so no need to worry about their permutations individually. Now, wherever we place S and L in 7 positions, S will be replaced in 10,20,40,50 order and likewise for L.
So out of 7 positions, we can place 3 larger nos. {L,L,L} in 7C3 ways=7!/4!*3!
(Which automatically includes combinations for choosing smaller 4 nos.)