In how many arrangements can a teacher seat 3 girls and 3 bo

Hi All,

These types of story-based permutation questions can usually be solved with a basic drawing and some multiplication.

Here, we're told to sit 6 children in a row (3 boys and 3 girls) and that two adjacent seats CANNOT have the same gender. We're asked for the total number of possible ways to seat the 6 children.

So, let's start with 6 chairs:

_ _ _ _ _ _

The first chair can have ANY of the children:

6 _ _ _ _ _

Whether you put a boy or a girl in that first chair, the second chair MUST have the opposite gender - there will be 3 of those children available:

6 3 _ _ _ _

From here, we just have to go "back and forth" with the 2 remaining boys and the 2 remaining girls:

6 3 2 2 1 1

Now, we just multiply the numbers: (6)(3)(2)(2)(1)(1) = 72 possible arrangements

Final Answer:

GMAT assassins aren't born, they're made,
Rich