Place the number of successes for each outcome into List 1. Place the corresponding probability of success on a single trial into List 2.
The number of distinguishable permutations is the total number of trials factorial divided by the product of each individual number of successes factorial. This is then multiplied by the product of each probability raised to the number of successes power.
(sum L1)! / prod (L1!) * prod (L2^L1)