  A fair clustering instance is given a data set $A$ in which every point is
assigned some color. Colors correspond to various protected attributes such as
sex, ethnicity, or age. A fair clustering is an instance where membership of
points in a cluster is uncorrelated with the coloring of the points.
  Of particular interest is the case where all colors are equally represented.
If we have exactly two colors, Chierrichetti, Kumar, Lattanzi and Vassilvitskii
(NIPS 2017) showed that various $k$-clustering objectives admit a constant
factor approximation. Since then, a number of follow up work has attempted to
extend this result to a multi-color case, though so far, the only known results
either result in no-constant factor approximation, apply only to special
clustering objectives such as $k$-center, yield bicrititeria approximations, or
require $k$ to be constant.
  In this paper, we present a simple reduction from unconstrained
$k$-clustering to fair $k$-clustering for a large range of clustering
objectives including $k$-median, $k$-means, and $k$-center. The reduction loses
only a constant factor in the approximation guarantee, marking the first true
constant factor approximation for many of these problems.
