The school playground is in the shape of a pentagon. There is a drinking fountain at each of the 5 corners of the playground. How many ways can someone walk from one drinking fountain to another drinking fountain?
5*4
To determine the number of ways someone can walk from one drinking fountain to another, we can use the concept of permutations.
First, we need to identify the number of starting points and the number of endpoint options.
In a pentagon, there are 5 corners where the drinking fountains are located. Therefore, there will be 5 possible starting points.
Now, for each starting point, we need to determine the number of possible endpoints. Since the person cannot return to the starting point or visit the same fountain twice, the number of possible endpoint options decreases by one as they move from one fountain to another.
Starting from any corner, the first person has a choice of 4 fountains to move to for the second step. Once at the second fountain, the person has 3 fountains to move to for the third step, and so on.
So, for each starting point, the number of possible endpoint options will be 4 for the second step, 3 for the third step, 2 for the fourth step, and finally, 1 for the fifth step.
Now, to calculate the total number of ways someone can walk from one drinking fountain to another, we need to multiply the number of starting points by the number of possible endpoint options for each starting point.
5 (starting points) × 4 (possible endpoints for the second step) × 3 (possible endpoints for the third step) × 2 (possible endpoints for the fourth step) × 1 (possible endpoints for the fifth step)
Calculating this expression gives us:
5 × 4 × 3 × 2 × 1 = 120
Therefore, there are 120 ways someone can walk from one drinking fountain to another on the school playground.