Repetition with Permutations-Number of Routes on a Grid Help?

How many routes are possible from A to B in this diagram:

Untitled photo by MightyOwned | Photobucket

I know it's a crap paint diagram. But you get the idea.

The answer is apparently 600. I tried doing 5!/(3!2!) X 6!/(3!3!) + 5!/(3!2!) X 6!/(4!2!) but no luck.

Please help.

Re: Repetition with Permutations-Number of Routes on a Grid Help?

Quote:

Originally Posted by

**MOMighty** How many routes are possible from A to B in this diagram: Untitled photo by MightyOwned | Photobucket

I know it's a crap paint diagram. But you get the idea.The answer is apparently 600. I tried doing 5!/(3!2!) X 6!/(3!3!) + 5!/(3!2!) X 6!/(4!2!) but no luck.Please help.

**WHY do you use all those **__special__ formats?

It makes it so hard to read.

And you are correct, that is a truly poor diagram.

Note that the two grids share two lattice points.

We need to count the paths through those two points: **inclusion/exclusion**.

$\displaystyle 2\left( {\frac{{5!}}{{3! \cdot 2!}}} \right)\left( {\frac{{6!}}{{3! \cdot 3!}}} \right) - \left( {\frac{{5!}}{{3! \cdot 2!}}} \right)^2 $