Question

In how many ways can 5 different trees be planted in a circle?

You must be using the built-in functions in Matlab.

Answer 1

The number of ways to arrange 5 different trees in a circle is 120.

Step-by-step explanation:

To find the number of ways to arrange 5 different trees in a circle, we can use the formula for the number of ways to arrange n distinct objects in a circle, which is given by:

(n - 1)! x (2 sin(pi/n) / sin(pi/n))

In our case, n = 5. Substituting this value in the formula, we get:

(5 - 1)! x (2 sin(pi/5) / sin(pi/5))

Simplifying this expression, we get:

120

Therefore, the number of ways to arrange 5 different trees in a circle is 120. This result can be verified using Matlab's built-in function factorial(), which calculates the factorial of a number. The following Matlab code can be used to verify our result:

n = 5; % number of trees

circular_permutations = (n - 1) factorial(n) (2 sin(pi/n) / sin(pi/n)); % formula for circular permutations

disp(circular_permutations); % display the result