  We prove a formula which generalizes both Onn's colorful determinantal
formula, related to Rota's basis conjecture, and Svrtan's $n!$ formula, related
to the Atiyah-Sutcliffe problem. In some cases, our formula allows us to prove
some results similar in spirit to the statement of Rota's basis conjecture. We
prove such a result using Svrtan's $n!$ formula, generalizing one of Svrtan's
arguments to a combinatorial setting.
