SOLUTION: Please show me how to do this problem. I got answers but they were not correct. [ a ][ ][ ][ ][ ][ ][ ] [ ][ ][ b ][ ][ ][ ][ ] [ ][ ][ ][ c ][

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Question 436404: Please show me how to do this problem. I got answers but they were not correct.
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If a route (with no backtracking) from A to Z is randomly chosen, what is the probability that the route passes through point B? Answer in fraction.
Given that a route passes through B, what is the probability that it also passes through point C? Answer in fraction.

Answer by robertb(5830) (Show Source):
You can put this solution on YOUR website!
I will assume that there are only 2 allowed movements: to the right and down.
Number of ways of going from a to b is 3C2 = 3. Number of ways of going from b to z is 5C4 = 5. The number of ways of going from a to z is 8C2 = 28.
==> the probability that the route passes through point B is .
==> Given that a route passes through B, the probability that it also passes through point C is .