  As is well-known, a generalization of the classical concept of the factorial
$n!$ for a real number $x\in {\mathbb R}$ is the value of Euler's gamma
function $\Gamma(1+x)$. In this connection, the notion of a binomial
coefficient naturally arose for admissible values of the real arguments.
  By elementary means, it is proved a number of properties of binomial
coefficients $\binom{r}{\alpha}$ of real arguments $r,\,\alpha\in {\mathbb R}$
such as analogs of unimodality, symmetry, Pascal's triangle, etc. for classical
binomial coefficients. The asymptotic behavior of such generalized binomial
coefficients of a special form is established.
