Permutation Problem

9 people are going on a trip in 3 cars that hold 2, 4, and 5 people respectively, in how many ways can the people travel while using all 3 cars?

any ideas?

Since there's only going to be one trip, there's consequently only one way.

I'll call them cars A,B,C respectively.

I) Car A has 1 person
    i) Car B has 4 people
        9*C(8,4) = 9*70 = 630
    ii) Car B has 3 people
        9*C(8,3) = 9*56 = 504
II) Car A has 2 people
    i) Car B has 4 people
        C(9,2)*C(7,4) = 36*35 = 1260
    ii) Car B has 3 people
        C(9,2)*C(7,3) = 36*35 = 1260
    iii) Car B has 2 people
        C(9,2)*C(7,2) = 36*21 = 756

Adding yields 4410 possibilities >> 1.

Well, if they were limiting themselves to, say, traveling on interstate highways in Virginia, there are 6 mainline routes and 10 loops and spurs from the mainline routes that they could travel, but you'd have to substract the roads with high radiation levels, to reduce the chance of permutations.