If I have N distinct points, how many different ways can I construct a set of distinct points? : <p>Lets say that I have 2 groups of distinct points. I'm trying to find all the possible different ways to travel between these points. In one group we have P1,P2 and in the other group P3,P4. Any point can be a starting point and can only end in the opposing group. I want to find a way to formalize how to find all combinations of these points. Each group can have an N distinct number of points, but I chose for each group to have 2 points. These are all the possible set of points from these two groups: </p>

<ul>
<li>Set 1: P1->P2->P3->P4</li>
<li>Set 2: P1->P2->P4->P3</li>
<li>Set 3: P2->P1->P3->P4</li>
<li><p>Set 4: P2->P1->P4->P3 </p></li>
<li><p>Set 5: P3->P4->P2->P1</p></li>
<li>Set 6: P3->P4->P1->P2</li>
<li>Set 7: P4->P3->P2->P1</li>
<li>Set 8: P4->P3->P1->P2</li>
</ul>

<p>The "->" denotes a path traveled. Therefore I have 8 distinct paths traveled. How do I formalize this though? I've tried thinking of exponents, and factorials... I'm a bit stuck right now.</p>
