Determine the number of permutations (p₁, p₂,...p₇) of 1,2, ...7; such that for all k 1≤k≤6, (p₁, p₂,... p_k) is not a permutation of (1,2, ...k); i.e., p₁≠1; (p₁, p₂) is not a permutation of (1,2), etc.

What would be the answer if we specify 1≤k<6 instead?