2018 AIME II Problem 11

Find the number of permutations of 1, 2, 3, 4, 5, 6 such that for each k with 1 \leq k \leq 5, at least one of the first k terms of the permutation is greater than k.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.