Question

A family consists of a grandfather,$6$ sons and daughters and $5$ grand children. They are to be seated in a row for dinner.The grand children wish to occupy two seats at each end and the grandfather refuses to have a grandchild on either side of him. In how many ways can the seating arrangements can be made for the dinner?

• A. $120$
• B. $100$
• C. $164$4
• D. $125$

Answer 1

Answer: (A)

$120$

$\begin{array}{ccccccccccc}s& s& s& s& s& s& s& s& s& s& s\\ 1& 2& 3& 4& 5& 6& 7& 8& 9& 10& 11\end{array}$

Seat number$1,2$ and $10,11$at the ends

are occpied by $4$ grand children

Number of ways ${=}^4{P}_4=24$ Ways

Grandfather cannot occupy seat $3$ and seat $9$

Number of ways of placing then $=5$

Total number of ways of averaging

$=24\times 5$

$=120$ Ways