Date: 10/24/1999 at 14:06:20 From: Roger Subject: Path Possibilities I have counted and calculated so many times and I'm still baffled. How many combinations of moves are there to get from point A to point B in the figure below, assuming that you can only move right and up? Also assume you are on the corners and not the lines. Point A is the very lower left corner, and B is the very upper right corner. _ _ _ _ B |_|_|_|_| |_|_|_|_| |_|_|_|_| _ _|_|_|_|_| |_|_| _|_|_| |_| A I know that if you take the number of possibilities of each set of squares and multiply them, then you get the solution. The small square has 2 possibilities. The second set of squares I think has 6. That is where I get lost. Thanks for your time! Roger
Date: 10/24/1999 at 16:22:23 From: Doctor Anthony Subject: Re: Path Possibilities Call a horizontal step H and a vertical step V. For the first stage you must take one of each, and you can arrange the letters H, V in two ways. For the second stage you must do 2 H's and 2 V's. You can arrange these four letters in 4! ----- = C(4,2) = 6 ways 2! 2! For the third stage you must do 4 H's and 4 V's. These eight letters can be arranged in 8! ----- = C(8,4) = 70 ways 4! 4! Therefore the total number of different paths is 2 x 6 x 70 = 840 - Doctor Anthony, The Math Forum http://mathforum.org/dr.math/
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