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

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, 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(52787) (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.

/////////////

From my post, learn two things:

            1)   How to make an analysis,

    and

            2)   How to use appropriate English words correctly in Math problems.

RELATED QUESTIONS
At a ski resort there are three different chair lifts that will take you to the top of... (answered by Alan3354)

A hiker hikes up a mountain 1mph slower than she hikes down the mountain. If it takes... (answered by checkley77)

Some hikers made the round trip on a mountain tail in 10 hours. It took three times... (answered by Alan3354)

There are 3 trails on the north face of Cowles Mountain and 2 trails on the south face.... (answered by ewatrrr)

I walk down the mountain 2mph faster than I walk up the mountain. If it takes me 3 hrs to (answered by ankor@dixie-net.com)

a hiker hikes up a mountain 1 mi/h slower than she hikes down the mountain. if it takes... (answered by mananth)

A mountain bike park has a total of 48 trails, 37.5% of which are beginner trails. The... (answered by macston)

A person walks to the top of a mountain at a rate of 4mi/hr and down the mountain the... (answered by macston)

a hiker hikes up a mountain 1 mi/h slower than she hikes down the mountain. if it takes... (answered by mananth)