Question 1149684
<pre>
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

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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</pre>