SOLUTION: If there are four roads from Ashville to Birchtown and three roads from Birchtown to Cedarburg, how many routes are there from Ashville to Cedarburg which go through Birchtown?

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Question 281467: If there are four roads from Ashville to Birchtown and three roads from Birchtown to Cedarburg, how many routes are there from Ashville to Cedarburg which go through Birchtown?
Answer by brucewill(101) About Me  (Show Source):
You can put this solution on YOUR website!
The answer is 12. Here's how I look at it:
Consider each of the paths from A to B, numbered 1, 2, 3 and 4.
Consider each of the paths from B to C, numbered 5, 6 and 7.
Using 1, you may then use 5, 6 or 7. 3 ways.
Using 2, you may then use 5, 6 or 7. 3 ways.
Do you see the pattern?
Simply 4 * 3 = 12.