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

assume just one configuration (boy in leftmost seat is not paired with girl1)

where boy and girl1 not paired. When boy is on leftmost, 10! ways girls can arrange.

For last 10 configurations 9! ways for rest of girls to arrange

total is 2 times 10!

assume two cases where boy and girl1 not paired, boy in leftmost or rightmost.

now for these two cases arrangements total 2 times 10!

plus now 9 configurations of paired boy and girl1, 9 times 9!

total is 2 times 10! plus 9 times 9!

assume just one configuration where boy and girl1 have to be paired, her to his left, boy in middle seat.. Then this case has 9! arrangements of other girls.

Plus for when the boy is not in middle, ten other places times 10! ways for girl to arrange.

total=9! + 10(10!).