Thread: How to calculate number of combinations required?

Hello all,

I have a 2 part question which I'm having some problems with. I've figured out the first part but am now stuck on the second and was hoping someone could please help me.

Say you have a lotto game with balls numbered from 1-43. 4 numbers are drawn and each number can only be used once. Now if I'm correct - to figure out how many possible combinations there are I used 43 C 4 = 43! / (43-4)! * 4! which gave me an answer of 123,410 unique 4 digit combinations.

Now the second part of my question and where I'm confused.

What if instead of selecting 4 numbers... I now selected 8 numbers. The question now is how many 8 digit number combinations is required to cover all the 123,410 unique 4 digit combinations at least once?

Can anyone help me with this?

Thanks in advance.