SOLUTION: There are three trails to the top of a mountain. In how many different ways can a person hike up and down the mountain if (a) she wants to take the same trail both ways? (b) she

Algebra ->  Probability-and-statistics -> SOLUTION: There are three trails to the top of a mountain. In how many different ways can a person hike up and down the mountain if (a) she wants to take the same trail both ways? (b) she      Log On


   

Question 1186515: There are three trails to the top of a mountain. In how many different
ways can a person hike up and down the mountain if
(a) she wants to take the same trail both ways?
(b) she can, highlight%28cross%28but_need_not%29%29 although it is not necessary, take the same trail both ways?
(c) she does not want to take the same trail both ways
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.

(a)  In three ways.   It is so OBVIOUS that does not require justifications.




(b)  She can select any of the 3 trails up and any of the 3 trails down.

     In all, there are 3*3 = 9 different ways.




(c)  For any of the three trails up, she can choose any of the two remaining trails down.

     In all, there are 3*(3-1) = 3*2 = 6 different choices.


Solved and thoroughly explained.


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