  We enumerate derangements with descents in prescribed positions. A generating
function was given by Guo-Niu Han and Guoce Xin in 2007. We give a
combinatorial proof of this result, and derive several explicit formulas. To
this end, we consider fixed point $\lambda$-coloured permutations, which are
easily enumerated. Several formulae regarding these numbers are given, as well
as a generalisation of Euler's difference tables. We also prove that except in
a trivial special case, if a permutation $\pi$ is chosen uniformly among all
permutations on $n$ elements, the events that $\pi$ has descents in a set $S$
of positions, and that $\pi$ is a derangement, are positively correlated.
