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

• Nov 13th 2012, 03:23 PM
MOMighty
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.

• Nov 13th 2012, 04:13 PM
Plato
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.

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