When two populations have the same probability density function, each outcome of \(n_{1}\) ranks for the first sample, out of the possible values \(1,2, \ldots, n_{1}+n_{2}\), is equally likely.

(a) Write out all of the possible outcomes when \(n_{1}=3=n_{2}\).

(b) Evaluate \(U_{1}\) at each of the outcomes and construct its probability distribution.