Question

A family consists of grandfather, $5$ sons and daughters and $8$ grandchildren. They are to be seated in a row for dinner. The grandchildren wish to occupy the $4$ seats at each end and the grandfather refuses to have a grand child on either side of him. The number of ways in which the family can be made to sit is

• A. 11360
• B. 11520
• C. 21530
• D. None of these

Answer 1

Answer: (B)

The total number of seats
$=1$ grand father $+5$ sons and daughters$+8$ grand children
$=14$
The grand children wish to occupy the $4$ seats on either side of the table $=4!$ ways
$=24$ ways
and grand father can occupy a seat in $(5-1)$ ways $=$ 4 ways
(Since $4$ gaps between $5$ sons and daughters)
and the remaining seats can be occupied in $5!$ ways
$=120$ ways ( $5$ seats for sons and daughters)
Hence, required number of ways
$=24\times 4\times 120=11520$