There are horse racing bets called Trifectas where you try to name the first three horses in a race in order. You can create all sorts of perms, from full perms, where each of your horses can finish 1st,2nd or 3rd, right down to complex ones where individual horses can be nominated as coming 1st or 3rd or 2nd and 3rd or just 3rd and so on. I want the calculation do to the following perm: 1. If x is the number of horses I choose to come 1st,2nd or 3rd 2. If y is the number of horses I choose to come just 2nd or 3rd 3. If z is the number of horses I choose to come just 3rd What is the number of permutations I would need ? Example: Say there are 15 runners (not that the number makes any difference), I choose 6 runners to come 1st,2nd and 3rd. This is a full perm and there are 120 permutations (x!/(x-3)!). Say I choose 6 runners to come 1st,2nd and 7 runners (inc the 6 to come 1st and 2nd) to come 3rd, there are 150 perms Say I choose 6 runners to come 1st, 7 runners (inc the 6) to come 2nd and 8 (inc the 7) to come 3rd there are 216 perms Hopefully you'll understand the question. I should think for someone who understands the maths of permutations better than me will find this trivial. This was added after 194 viewings of the project. I'm amazed that after so many viewings I've had no rated bids at all. I certainly didn't think the maths would be that difficult and still don't think it is. Aren't there any decent mathematicians in the world these days or is this the wrong place to look ? This was added after 440 views of the project and still no sensible messages or bids. This is becoming embarrassing and certainly not what I expected from vworker. Is it really that difficult ? Obviously it is for me but I would have thought there would have been at least 1 good mathematician out there. Seems like I'm asking in the wrong place.