Answer: 24
Step-by-step explanation:
We know that the permutation in a circle is known as circular permutation.
To calculate the circular permutations, we need the formula below:
[tex]C=(n-1)![/tex]
Given: The school playground is in the shape of a pentagon. There is a drinking fountain at each of the 5 corners of the playground.
Then , the number of ways can someone walk from one drinking fountain to another drinking fountain is given by :-
[tex](5-1)!=4!=4\times3\times2\times1=24[/tex]
Hence, the number of ways can someone walk from one drinking fountain to another drinking fountain is 24.
You can use the fact that a person can firstly be on anyone of the 5 corners. And then can choose the rest of the 4 corners to reach other drinking fountain. And then can use the rule of multiplication from combinatorics.
The total number of ways someone can walk from one drinking fountain to another drinking fountain for the given case is 20
If a work A can be done in p ways, and another work B can be done in q ways, then both A and B can be done in [tex]p \times q[/tex] ways.
Remember that this count doesn't differentiate between order of doing A first or B first then doing other work after the first work.
Thus, doing A then B is considered same as doing B then A
Since a person can stand on any of the 5 fountains, thus 5 ways of doing so.
Then there are 4 fountains left for that person to choose from. Thus, there are 4 ways of doing so.
Using rule of product, we have:
Number of ways in which someone can walk from one drinking fountain to another drinking fountain for the given case = [tex]5 \times 4 = 20[/tex]
Thus,
The total number of ways someone can walk from one drinking fountain to another drinking fountain for the given case is 20
Learn more about combinations and permutations here:
https://brainly.com/question/11958814
