Say I have a set of numbers 1 through N, E.g. {1,2,3,4,5,6}
I want to find the number of derangements, but for e.g the first 4 places {a,b,c,d} where there are of course the numbers 1 through 4 that will not be in its initial position, but there is an extra case of numbers here of 5 and 6 which can be put in any place. e.g in this problem a valid 'derangement' type of set could be {6,5,4,3} but so could a normal derangement such as {4,3,2,1}.
Im not sure how to start this since I cannot think of a way to include 5 and 6 but excluding the fact that its not a derangement set of size 5 and 6.