Counting Question

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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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|dw:1440284134239:dw|
\(\large \color{black}{\begin{align} & \normalsize \text{The Red and Green lines are perpendicular to each other}\hspace{.33em}\\~\\ & \normalsize \text{Find the number of shortest paths to go from A to B.}\hspace{.33em}\\~\\ & \normalsize \text{Find the total number of paths to go from A to B.}\hspace{.33em}\\~\\ & \normalsize \text{(Assume the points are equidistant)}\hspace{.33em}\\~\\ \end{align}}\)
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I'm on iPad , cannot draw out the paths, b to me , there are 2 shortest ways , and their weight is 6
I will go look at my graph theory book and I am sure I will find something.
are u sure its 6
Go, diagonal fromA, 3 times, then go straight to B 3 more
there are algorithms for this, that would be a pain to teach on here. google Dijkstra's algorithm
Assume each of the 6 red spaces have the same distance as the 3 green spaces, Number of paths = 9!/(6!3!)=84 ways
diagonal?
along the lines, if the question was for me.
Djikistra algorithm finds shortest distance, where as i need the number of shortest paths
Go to the right of A 1, then, diagonal, then right,then,diagonal,repeat 1 more time to get B
Use adjacent matrix to find them out. It works also
Why not diagonal? Since it is = right+ vertical up.?
answer is 210 for 1st one
the path has to along the lines can't jump diagonally
Ohoh, so I'm wrong, hehe.
|dw:1440285501178:dw| an example
Yes that is right, there is some algorithm that will tell you.
It's like a permutation with 9 objects, 3 red and 6 green. RGRGRGGGG RRRGGGGGG .... Using the multinomial theorem, the number of ways would be 9!/(6!3!)
thanks @mathmate ur anwers was correct
You're welcome! :)

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