The bivariate inverted hypergeometric function type I distribution is defined by the probability density function proportional to $ x_1^{\nu_1-1} x_2^{\nu_2-1} \left(1 + x_{1} + x_{2}\right)^{-(\nu_1+\nu_2+\gamma)}$\linebreak $ \leftidx{_2}{F}{_1} (\alpha,\beta;\gamma;(1+ x_{1}+x_{2})^{-1} )$, $x_1>0$, $x_2>0$, where $\nu_1$, $\nu_2$, $\alpha$, $\beta$ and $\gamma$ are suitable constants. In this article, we study several properties of this distribution and derive density functions of $X_1/X_2 $, $X_1/(X_1+X_2)$, $X_1+X_2$ and $ X_1 X_2 $. We also consider several other products involving bivariate inverted hypergeometric function type I, beta type I, beta type II, beta type III, Kummer-beta and hypergeometric function type I variables.