1. ## Combination Question

9 people drive into a parking lot, 4 are boys and 5 are girls. They decide to park in a straight row of 9, if none of the girls park next to each other, how many different parking arrangements are there?

Thanks

2. Originally Posted by RicLang
9 people drive into a parking lot, 4 are boys and 5 are girls. They decide to park in a straight row of 9, if none of the girls park next to each other, how many different parking arrangements are there?
What if they are in only two cars?

3. Originally Posted by Plato
What if they are in only two cars?
They are each in one car.

4. Hello, RicLang!

9 people drive into a parking lot, 4 are boys and 5 are girls.
They decide to park in a straight row of 9 spaces.
If none of the girls park next to each other, how many different parking arrangements are there?

If the girls are non-adjacent, there is ONE arrangement of the genders: .$\displaystyle GBGBGBGBG$

Then the five girls can be arranged in: .$\displaystyle 5!$ ways.
The four boys can be arranged in: .$\displaystyle 4!$ ways.

Therefore, there are: .$\displaystyle (5!)(4!) \:=\:(120)(24) \:=\:2880\text{ arrangements.}$

5. Thanks alot!