I'm racking my brain with this one - precalculus was years ago, so combination sets with multiple groups seem a little hard to manage.Let's establish this - if ranking all the players 1-11, there are exactly 39,916,800 ways to arrange them. However, we're not arranging them 1-11 - we're splitting them into two five-person groups with one left over.
There are exactly six ways to arrange the teams so they are men vs. women - all five women on one team, and five of the six men on the other, and the only variable is which man sits out.
So we have our numerator - six. To get the denominator, it's a little harder. So I Googled "combination calculator" with this thought in mind - we can simplify this equation by doing the following: We pick ONE of the teams, understanding that, with every combination we pick for that team, say, the yellow team, we can fill the blue team with six possible combinations.
This allows us to simplify a bit - since we established that there are six possibilities for a men vs. women contest, and we have also established that, with each yellow team drawn, we have six possible blue teams, these sixes cancel each other out.
Therefore, the equation is simple: How many five-player combinations can we get out of an 11-player group?
According to www.calculatorsoup.com, the answer to that question is 462. Therefore, the probability of a men vs. women contest is 1/462, or approximately a 0.216% chance.
That's not to say that Burnett arranged this or that Jiffy did - the arrangement that happened is a coincidence, but it's just as likely as the other 2,771 combinations of teams that could have occurred.
Also, a men vs. women split was interesting for about four seconds. The challenge relied a lot on physical strength, and at least in this cast, the men were physically more powerful than the women. Right away, one could tell the men would win.
So I wouldn't call it producer manipulation just yet.