We discuss the capacity region of a degraded broadcast channel (DBC) formed from a channel that randomly permutes input packets by selecting a permutation according to a probability distribution. Starting from the known capacity region expression for the DBC, we give an explicit outer and inner bound to the capacity region which are shown to be equal for the cases of 2 and 3 packets. The work extends previous results which considered the case where the permutation was selected uniformly from the set of all permutations. The results are useful in determining fundamental rate delay tradeoffs when transmitting temporally ordered content over multipath routed networks.