SOLUTION: Suppose there are ten roads from City A to City B and five roads from City B to City C. a. How many routes are there from City A to City C passing through City B? b. How many ro

Algebra ->  Permutations -> SOLUTION: Suppose there are ten roads from City A to City B and five roads from City B to City C. a. How many routes are there from City A to City C passing through City B? b. How many ro      Log On


   

Question 1061885: Suppose there are ten roads from City A to City B and five roads from City B to City C.
a. How many routes are there from City A to City C passing through City B?
b. How many road-trips are there of the form A-B-C-B-A?
c. How many road-trips are there of the form A-B-C-B-A in which on return to trip we do not reverse the original route from A to C?
Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
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Suppose there are ten roads from City A to City B and five roads from City B to City C. 

a.  How many routes are there from City A to City C passing through City B?  10*5 = 50.

b.  How many road-trips are there of the form A-B-C-B-A?                    (10*5)*(5*10) = 50%5E2 = 2500.

c.  How many road-trips are there of the form A-B-C-B-A in which on 
    return to trip we do not reverse the original route from A to C?        (10*5)*(4*9) = 50*36 = 1800.