A Question of Probabilities and Combinations

[ThunderAeroI]

Lets say you have seven lists, and each list has a different number of elements:

L1: 3
L2: 2
L3: 8
L4: 10
L5: 4
L6: 11
L7: 2

How would I determine the maximum number of different combinations that are possible if you must select one and only one element from each list?

I promise this isn't math homework, its something for a story I am working on.

 

[DonIago]

Isn't that just 3 x 2 x 8....

 

[Asbo Zaprudder]

The number of combinations without regard to order for which order you pick from each list = L1 x L2 x L3 x L4 x L5 x L6 x L7 = 42,240 in this case.

Permutations are a little more tricky as you can pick from the lists in random order. The total number of ways of ordering the lists is N! (N factorial), where N is the number of lists, so in this case 7! = 5,040. So the total number of permutations is 5,040 x 42,240 = 212,889,600.