So just how unlikely was the draw for our debates?

Warren either got screwed (I think) or she lucked out (some argue that) but Warren is the only member of the top five on her night while the other 4 are on a different night. Sounds like a lightning strike or finding a four leaf clover in your lawn. Well, not so much.

Let's start with the question of how unlikely was it that Warren would be alone on her night. You are choosing 4 people from a group of 8. Thus you have 8 choices for the first slot, 7 for the second, 6 for the third, and 5 for the fourth and the fundamental rule of counting says we should multiply those numbers to get a total number but this would over count the combinations since order doesn't matter. We are counting Biden, Sanders, Buttigieg, Harris as a different group than Sanders, Buttigieg, Harris, Biden and they aren't different. Thus we have to divide by the number of ways those four candidates can be ordered, 4 for the first slot, 3 for the second, 2 for the third, and 1 for the last. So we get (8*7*6*5) / (4*3*2*1) which reduces to 70. So there was a 1 in 70 chance of this happening to Warren in particular. That is a bit over 1%, not exactly a rare event.

Now to expand to this happening to one of the people in 2nd through 5th place. That would be 4/70 or over 5%. So an over 1/20 chance that one of our four candidates who are in 2nd through 5th place would get an isolated debate. All to be 'fair' to the likes of Andrew Yang who rode right wing money to get his space and Marianne Willamson who is a modern day snake oil salesman. And of course there is a 5% chance of this happening in the 2nd debate too.