Question 13068
Hi,

I found this quite an interesting question, because I couldn't think of a straight forward way to solve it. Obviously a brute force solution is out of the question as there are 120 combinations. This is the best I could come up with:

We know that A must be before B so there are 3 regions in which we can place the other people region p(left of A), q(between A and B), and r(right of B).

<p>p A q B r</pre>

We have 3 pieces to place in these regions, the ways we can do that are:

<table border="1"><tr><th>p</th><th>q</th><th>r</th></tr><tr><td>3</td><td>0</td><td>0</td></tr><tr><td>2</td><td>1</td><td>0</td></tr><tr><td>2</td><td>0</td><td>1</td></tr><tr><td>1</td><td>2</td><td>0</td></tr><tr><td>1</td><td>1</td><td>1</td></tr><tr><td>1</td><td>0</td><td>2</td></tr><tr><td>0</td><td>3</td><td>0</td></tr><tr><td>0</td><td>2</td><td>1</td></tr><tr><td>0</td><td>1</td><td>2</td></tr><tr><td>0</td><td>0</td><td>3</td></tr></table>

In each of these configurations CDE can be assigned any way you like (3! ways) and there are 10 configurations so that makes 10*3!=10*6=60 different ways.