People sitting around a table question

Hello forum. I need help with this particular question.

10 males and 10 females and one child. They need to sit around a table, with the one and only condition that no two males can sit next to each other.

There are no conditions no the child, it's just there to make things complicated, and for me it indeed has.

Where I am so far is, take two guys and think of them as one person, and calculate the chance that indeed two guys sit right by each other, and subtract this from the overall number of possible seatings.

Chance two guys sit by each other: 18! [19!/19] (19 people around a circle)

Chance of overall options without conditions: 20! [21!/21] (21 people around a circle with no conditions)

So my answer is 20!-18! but I think it is wrong, can somebody please help?

Re: People sitting around a table question

Quote:

Originally Posted by

**ineedhelplz** 10 males and 10 females and one child. They need to sit around a table, with the one and only condition that no two males can sit next to each other.

There are no conditions no the child, it's just there to make things complicated, and for me it indeed has.

**EDIT**

There are twenty-one chairs around the table. Pick two of them in such a way so that they are together . There are $\displaystyle 10!$ ways to seat the ten men in the starting at the right of the pair and skipping ever other chair .

At this point the table is no longer circular( it is ordered by the men). Thus there are $\displaystyle 11!$ ways to seat the remaining eleven people.

What is the final answer?