1 .
Consider 12 boys, 17 girls, and 25 dogs. How many ways are there to arrange them on a line if
- all boys stand next to each other,
- all girls stand next to each other,
- all dogs stand next to each other,
- none of the boys are standing next to any of the girls.
(a)
$12! + 17! + 25!$
(b)
$(12!)(17!)(25!)$
(c)
$2(12!)(17!)(25!)$
(d)
$2(12! + 17! + 25!)$