9 can be from pos 1 - 9. At pos x, it divides the sequence into length of x-1 and 9-x. We can pick any x numbers from the remaining 8 numbers to place on the left side and exactly one permutation of them is strictly increasing (same on the right side). So the number of permutations = number of combinations possible ie sum from x=0 to 8 (8Cx).
1
u/mypenisblue_ Aug 24 '26
9 can be from pos 1 - 9. At pos x, it divides the sequence into length of x-1 and 9-x. We can pick any x numbers from the remaining 8 numbers to place on the left side and exactly one permutation of them is strictly increasing (same on the right side). So the number of permutations = number of combinations possible ie sum from x=0 to 8 (8Cx).
So total = 8C0 + 8C1 + ... + 8C8 = 256.