# Thread: data staff....

1. ## data staff....

In how many possible ways can a family of five be seated in a passenger car if either two or three people sit in the front seat and only tow members can drive? (ps : as my understanding, totally the can contained 6 seats, 3 in front, and 3 in the back)

Please leave your solutions as well.... thank u very much

2. Originally Posted by ives
In how many possible ways can a family of five be seated in a passenger car if either two or three people sit in the front seat and only tow members can drive? (ps : as my understanding, totally the can contained 6 seats, 3 in front, and 3 in the back)

Please leave your solutions as well.... thank u very much
Let's do some surgery and disect this problem!

Two different people can drive, so this gives us two possibilities. Of those two possibilities, there are $4!$ different ways you can arrange the other four people. This applies to Person A and Person B, so we have $2*4!$ ways that the family can be arranged. Lastly, we can have two or three people in the front, so this once again doubles out possibilities to give us a final answer of $4*4! = 96$ arrangements.

Let me know if I missed anything!