SOLUTION: Twenty students, ten male and ten female, are to travel from school to the sports ground. Eight of them go in a minibus, six of them in cars, four of them on bikes and two walk. I

Question 1149684: Twenty students, ten male and ten female, are to travel from school to the sports ground. Eight of them go in a minibus, six of them in cars, four of them on bikes and two walk.
In how many ways can they be distributed if none of the boys walk?

Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!

We always choose the most restrictive things first.  
The most restrictive are the 2 walkers, since they are girls not boys. 

We choose the 2 walkers: 10 girls CHOOSE 2 = 10C2 = 45 ways.
That leaves 18 students.
We choose the 8 minibus riders: 18 students CHOOSE 8 = 18C8 = 43758 ways.
That leaves 10 students.
We choose the 6 car riders: 10 students CHOOSE 6 = 10C6 = 210 ways
That leaves 4 students.
We choose the 4 bike riders: 4 students CHOOSE 4 = 4C4 = 1 way.

Answer: (45)(43758)(210)(1) = 413513100

--------------------

To show that it doesn't matter, after the most restrictive things are chosen
first, what order the other non-restrictive things are chosen in, for look at
this different order:

We choose the 2 walkers: 10 girls CHOOSE 2 = 10C2 = 45 ways.
That leaves 18 students.
We choose the 4 bike riders: 18 students CHOOSE 4 = 18C4 = 3060 ways.
That leaves 14 students.
We choose the 6 car riders: 14 students CHOOSE 6 = 14C6 = 3003 ways
That leaves 8 students. 
We choose the 8 minibus riders: 8 students CHOOSE 8 = 8C8 = 1 way.

Answer: (45)(3060)(3003)(1) = 413513100

Different numbers were multiplied but the answer is exactly the same.

Edwin

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