$18$ guests have to be seated, half on each side of a long table. Four particular guests desire to sit on one particular side... 
$18$ guests have to be seated, half on each side of a long table. Four particular guests desire to sit on one particular side and three others on the other side. Determine the number of ways in which the sitting arrangement can be made.

I have found two (same) answers in two different format on two different websites. I have doubts in both.
One format is $^9P_4\times^9P_3\times11!$. Here, they are arranging four particular guests and three particular guests and then arranging the remaining $11$ guests. My doubt is: shouldn't we multiply by $^2P_1$ as well because the four or the three particular guests can be seated on either side of the table?
The other format of the answer is $^{11}C_5\times9!\times9!$. Here, $5$ comes from $9-4$, right? $4$ being the four particular guests. So, are they saying they seated the four and the three particular guests and then chose $5$ guests out of the remaining $11$ to be seated with the four particular guests and then arranged all of them on their respective side of the table? Once again, does it cover the possibility that the four particular guests could sit on either side of the table?
 A: "My doubt is: shouldn't we multiply by 2P1 as well because the four or the three particular guests can be seated on either side of the table?"
No. The question says:

Four particular guests desire to sit on one particular side and
three others on the other side

i.e.: four want to sit on the left side and the other three wants to sit on the right side, or: four want to sit on the right side and the other three want to sit on the left side, but not both scenarios at the same time (i.e. they do care/it does matter which side they're on). It's either one scenario or the other.
In other words, if you ask the four, "where do you want to sit?" They won't collectively answer: "I don't mind which side, so long as we are all on the same side, and the other three are on the other side". They will answer either, "Us four want to sit on the left side (and therefore the other three want to sit on the right side)", or they will answer, "Us four want sit on the right side (and therefore the other three want to sit on the left side)".
