<p>This paper points out a vast family of multivariate distributions where the variables involved are pairwise independent, but mutually dependent. The corresponding family of trivariate distributions, with pairwise independent marginals, is studied in detail. Continuous distributions with such a property have not been much studied in the available literature. This distribution may help to model situations where two variables have a joint effect on a third variable, even though the individual effects of the two variables on the third variable are negligible. The paper also studies the joint distribution of bivariate concomitants of order statistics arising from the trivariate distribution. To validate and support the theoretical findings, a simulation study is conducted. In addition, practical applicability of the study is reinforced using a real-life dataset, ensuring that the results have both theoretical significance and real-world relevance.</p>