A boy and 10 girls must sit in a row. how many ways can they sit if the boy sits in the middle a difficult girl always sits on his left side?

Question

A boy and 10 girls must sit in a row. how many ways can they sit if the boy sits in the middle a difficult girl always sits on his left side?

Answer 1

If the boy is seated in the middle, there are 11 positions in the row: one in the middle and five on each side.

We can start by placing the boy in the middle position. Then, we can choose one of the 10 girls to sit to his left (since a specific difficult girl is always seated to his left) and arrange the remaining 9 girls and the boy on the right side and left side of the difficult girl, respectively.

The number of ways to arrange 9 people in a row is 9!, and the number of ways to arrange the boy and the difficult girl to his left is 2 (since they occupy fixed positions). Therefore, the total number of seating arrangements is:

11 * 2 * 9! = 11,259,072

So, there are 11,259,072 ways for the boy and 10 girls to sit in a row if the boy sits in the middle and a difficult girl always sits on his left side.