The question MACHINE Lendi to you but trust me the solution is very short.

Latest resume that there are eight chairs. The chairs at the extreme ends are occupied by the grandchildren according to the question.

So the number of chairs remaining is equal to 6. It is clearly MENTIONED in the question that the grand mother has to SIT with her children on either SIDE.

Because of this condition we cannot make the grandmother sit right next to any of the Grand childrens.

Therefore number of chairs available for grandmother is equal to 4.

Now from those 4 chairs grandmother will be sitting at any one chair. Which means the remaining 5 chairs are free for the five childrens.

So it is clear that the grandmother and the children can sit in 4 x 5 = 20 ways.

Now the grandchildren at the extreme ends can sit in two ways by exchanging the positions. i.e. 20 x 2 = 40 ways

Therefore, in 40 ways can the seating arrangement be made such that the grandchildren occupy both the seats at the end and the grandmother sits with her children on either side of her.