可能なすべての男性女性の組み合わせを見つける

A社とB社の2社が12の異なる会議に参加する予定です。私たちは男性と女性が参加していることに基づいて、すべての会議（どの砂漠を得るか）の成果を知っています。

ルール：

1. There are total 12 conferences, C1 to C12
2. Participated companies are A and B
3. Each company's 12 employees are participating these conferences: A1 to A12 and B1 to B12
4. Each conference has 3 participants, 1 is from company A and 2 are from B
5. Each participants get either ice-cream or chocolate based on the gender combination of the participants in each conference. => If all the three participants in one conference are female or two are male and 1 is female, then each in that particular conference will get chocolate. => If all three participants in a conference are male or two are female and 1 is male then they will get ice-cream.

6. Below is the list of conference wise participants and what they got.

   C1 => A12, B1 , B11 => ice-cream
   C2 => A11, B2 , B4 => chocolate
   C3 => A10, B3 , B10 => chocolate
   C4 => A9 , B4 , B12 => ice-cream
   C5 => A8 , B5 , B7 => chocolate
   C6 => A7 , B6 , B5 => ice-cream
   C7 => A6 , B7 , B8 => ice-cream
   C8 => A5 , B8 , B1 => ice-cream
   C9 => A4 , B9 , B6 => chocolate
   C10 => A3 , B10, B2 => ice-cream
   C11 => A2 , B11, B9 => chocolate
   C12 => A1 , B12, B3 => ice-cream

上記のルールから、上記のシナリオに基づいて男性と女性の従業員とジェンダーの組み合わせがいくつあるかを調べます。

以下は1つの組み合わせ例です。以下の組み合わせは完全に間違っているので、このパズルを解く際には考慮しないでください。これは組み合わせの定義のみを与えます。
A1 =男性
A2 =女性
A3 =女性
A4 =男性
。
。
A12 =女性
B1 =女性
B2 =男性
。
。
B12 =女性