Question 953794: combinatorial analysis
there are four bus lines between a and b; three bus between b and c. in how many ways can man travel
a.by bus from a to c by way of b?
b. roundtrip by bus from a to c by way of b?
c. roundtrip by bus from a to c by way of b, if he doesnt want to use a bus line more than once?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 4 bus lines between a and b.
3 bus lines between b and c.
the number of possible combinations between a and c going through b are 4 * 3 = 12.
if you're talking about round trip, he has 12 possible ways to get there and 12 possible ways to get back, so the total possible ways is 12 * 12 = 144.
if he doesn't want to take the same route back, then:
possible ways to get there is 4 * 3 = 12
possible ways to get back is 3 * 2 = 6
total possible ways is 12 * 6 = 72.
possible ways to get back is 3 * 2 because he can't use the same route coming back then he did going. he therefore has to take one possible route away from the b to a section and 1 possible route away from the c to b section.
that results in 3 possible ways from b to a and 2 possible ways from c to b.
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