Question: 2017 Winter Midterm - 3

Author: Michiel Smid

Let $b \geq 1$ and $g \geq 1$ be integers. Consider $b$ boys and $g$ girls. How many ways are there to arrange these kids on a line such that the leftmost kid is a girl or the rightmost kid is a boy?

(a)

$(b+g)! - b \cdot (b+g-1)! -\ $ $ g \cdot (b+g-1)!$

(b)

$g \cdot (b+g-1)! + b \cdot (b+g-1)!\ -$ $ b \cdot g \cdot (b+g-2)!$

(c)

$g \cdot (b+g-1)! + b \cdot (b+g-1)!\ -$ $ b \cdot g \cdot (b+g-1)!$

(d)

$(b+g)!$