EDIT: Ah, we all make mistakes. Thanks to Deagez for pointing out my error. Solution fixed below.
These problems might be too long to write out every combination, so it's best to break the problem down into its component parts.
First, one of the two parents must drive, and they are identical otherwise. So, let's put one of them in the driver's seat and find all possibilities with this restriction, and then multiply by 2, since we could sub one parent for the other.
Now, let's look at the front seat. If one of the daughters sits there, there is no way for the daughters to be sitting next to each other, and so any combination of the remaining three in the back is fine. There are six possibilities in this case. There are also another six possibilities for the other daughter sitting in the front seat.
If the other parent is in the front seat, there is two possible backseat combo (son must be in the middle, and the daughters can be swapped). Likewise, if the son is in the front seat, only two backseat combos with the mother in the middle exists.
So, total for one particular parent in the driver's seat = 6 + 6 + 2 + 2 = 16. Multiply by 2 for the other parent, and we have our answer, 32.
Guessing tip on the test: If you can't run through this type of problem quickly, try to just find a range. If there were no restrictions at all, there would be 5! = 120 possibilities, but we know that only 2/5 of these are valid (parent in the driver's seat), so that leaves 48. More restrictions only bring the number of possibilities down, so there must be fewer than 48 possibilities, leaving only two answers. Hey, 50-50 isn't horrible...
Last edited by Feep on Fri Apr 17, 2009 3:38 am, edited 1 time in total.
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