How many ways can six people be seated at a round table with restrictions?

Question

I'm learning these two subjects, and there is a question to which I can not find an answer:

1. given $2$ groups of people :

$X = \{A,B,C\} $ and $Y = \{D,E,F\}$

Find how many arrangements of seats at a round table there can be if:

• $A$ can not seat near anyone belong to $Y$
• only $F$ from $Y$ can seat near $B$
• $E$ needs to seat near $D$ and $C$

How can I solve this question?

I don't know how to approach this.

Thanks

Answer 1

This isn't really a combinatorics question. The order around the table is completely determined by the constraints, with only the direction around the table left as a free choice, giving two options (when rotations are taken as equivalent).

Answer 2

Logically, the only place where $A$ can seat is between $B$ and $C$ so that gives us two possible arrangements. $F$ should be next to $B$, $E$ should be next to $C$ so there are not many possibilities for other arrangements.