Class 11

Math

Algebra

Permutations and Combinations

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?

- $120$
- $100$
164$4 - 125$$

$s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 s11 $

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

$=24×5$

$=120$ Ways