Question

There are seven roads that lead to the top of a hill. How many different ways are there to reach the top and to get back down, if the uphill and downhill roads are different?

Answer 1

Given are the seven roads (say A, B, C, D, E, F, and G) that lead to the top of a hill. We need to select a road to reach the top and then it says to select different road to get back down.

First of all, we can select any one road from seven roads. So, we have 7 ways to go to the top.

After reaching the top, this first road gets eliminated from selection and now we have only Six roads to come downhill. So, we have 6 ways to get back down.

So, total number of ways = 7 × 6 = 42 ways.

So, there are 42 different ways are there to reach the top and to get back down, if the uphill and downhill roads are different.