Eighteen 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 other side. If the number of ways in which the sea

Question

Eighteen 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 other side. If the number of ways in which the seating arrangements can be made is ( p !) ( p + 1 )! 11 ∣ × ( 9 ! ) 2 ​ . Then the value of ′ p ′ is

TestHub · Accepted Answer

Out of 18 guests half i.e., 9 to be seated on side $A$ and rest 9 on side $B$ .

Now out of 18 guests, 4 particular guess desire to sit on one particular side say side

$A$ and other 3 on other side $B$ . Out of rest $18 - 4 - 3 = 11$ guests

we can select 5 more for side $A$ and rest 6 can be done in

$^{11} C_{5}$ ways and 9 guests on each side of table can be seated in $9! 9!$ ways.

Thus there are total $^{11} C_{5} 9! 9!$ arrangements.

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