  This paper examines the classical matching distribution arising in the
"problem of coincidences". We generalise the classical matching distribution
with a preliminary round of allocation where items are correctly matched with
some fixed probability, and remaining non-matched items are allocated using
simple random sampling without replacement. Our generalised matching
distribution is a convolution of the classical matching distribution and the
binomial distribution. We examine the properties of this latter distribution
and show how its probability functions can be computes. We also show how to use
the distribution for matching tests and inferences of matching ability.
