Mack the bug starts at (0,0) at noon and each minute moves one unit right or one unit up. He is trying to get to the point (5,7). However, at (2,3) there is a spider that will eat him if he goes through that point. In how many ways can Mack reach (5,7)?
+130477 The number of ways to get from (0, 0) to (5, 7) moving in this manner is given by
(7 + 5) ! / (7! 5!) = 12! / (7! 5! ) = 792 ways
From these, we want to subtract the ways to get from (0, 0) to (2, 3)
This is given by
(3 + 2)! / (3! 2!) = 5! / (3! 2!) = 10 ways
So 792 - 10 = 782 routes
If you would explain one of the factorials it would be greatly appreciated. I don't really understand how they are generated ,say, for the number of routes to the spider.
+130477 I'm gonna' be honest, Anonymous....I "borrowed" this "formula" from one of our fellow posters, Nauseated, based on his answer to a problem just last week....I haven't had time to digest the rationale behind it, yet.
However.......here is his "non-technical" explanation.....if you care to look at it....
{It's the fourth answer from the bottom}.........http://web2.0calc.com/questions/each-small-square-has-a-side-length-of-one-unit-how-many-distinct-paths-of-six-units-are-there-from-a-to-b
This helped a little.http://betterexplained.com/articles/navigate-a-grid-using-combinations-and-permutations/
