Permutation & Combination help.

Apr 2010
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1. Given the diagram below, determine the number of pathways starting from A and moving to B along the gridlines if a pathway must always move closer to B.

pathways_03_hole.png


2. Given the diagram below, determine the number of pathways starting from A and moving to B along the gridlines if a pathway must always move closer to B.

7-4_quiz_complexpathways_c_cbel.png



Please help me with these questions I do not know how to do it.
 

Opalg

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1. Given the diagram below, determine the number of pathways starting from A and moving to B along the gridlines if a pathway must always move closer to B.
Starting from B, and working upwards and to the left, label each node with the number of paths from there to B.

For the nodes immediately to the left of B, and also for those immediately above B, there is only one available path to B. For each other node, the number of paths from that node is the sum of the numbers for the nodes next to it on the right and below. Working all the way back to the node at A, you get the answer 34 for the total number of paths.

Use the same method for the other part of the question.
 

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Dec 2009
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1. Given the diagram below, determine the number of pathways starting from A and moving to B along the gridlines if a pathway must always move closer to B.

View attachment 17006


2. Given the diagram below, determine the number of pathways starting from A and moving to B along the gridlines if a pathway must always move closer to B.

View attachment 17007



Please help me with these questions I do not know how to do it.
Hi danield3,

here's another way..

In part 1, the diagram is symmetrical.
If we find the number of ways to go from A to C
and the number of ways to go from C to B,
given the directional restriction,
we can multiply these to find the number of ways that require at least one internal path,
in going through C.
Add the external path.
The exact same number of ways are available in going across the top first.

In part 2, the ways can be summed independently from A to B through C,
A to B through D while avoiding E, and A to B through E avoiding D.
 

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