Combinations with different probability

Lets say I have 5 independent events (A-E):

Pr(A) = 0,5
Pr(B) = 0,4
Pr(C) = 0,3
Pr(D) = 0,2
Pr(E) = 0,1

One "attempt" per event. I want to calculate the probability of three succesful events.
I do it like this:

Pr(A)*Pr(B)*Pr(C) * (1-Pr(D)) * (1-Pr(E))... for all different combinations.

But thats a lot of calculation and if I want more events it will get out of hand.
Perhaps there is some program or code that can do theese type of calculations?