Prove that

[[math]] \sum_{j,k} \biggl(\frac 1{3^n}\frac{n!}{j!k!(n-j-k)!}\biggr) = 1\ , [[/math]]

where the sum extends over all non-negative [math]j[/math] and [math]k[/math] such that [math]j + k \le n[/math]. Hint: Count how many ways one can place [math]n[/math] labelled balls in 3 labelled urns.