  We present concentration inequalities on the multislice which are based on
(modified) log-Sobolev inequalities. This includes bounds for convex functions
and multilinear polynomials. As an application we show concentration results
for the triangle count in the $G(n,M)$ Erd\H{o}s--R\'{e}nyi model resembling
known bounds in the $G(n,p)$ case. Moreover, we give a proof of Talagrand's
convex distance inequality for the multislice.
  Interpreting the multislice in a sampling without replacement context, we
furthermore present concentration results for $n$ out of $N$ sampling without
replacement. Based on a bounded difference inequality involving the
finite-sampling correction factor $1- n/N$, we present an easy proof of
Serfling's inequality with a slightly worse factor in the exponent, as well as
a sub-Gaussian right tail for the Kolmogorov distance between the empirical
measure and the true distribution of the sample.
