Respuesta :
Answer:
N = 32 ways
the dispatcher can send the police officers to the scene of the caller in 32 ways.
Step-by-step explanation:
Given;
Total number of officers = 5
The total number of ways the dispatcher can send the police officers is the sum of the number of ways of sending each of no officer, one officer, two officers, three officers, four officers, or all five officers.
N = 5P0 + 5P1 + 5P2 + 5P3 + 5P4 + 5P5
N = 1 + 5 + 10 +10 + 5 + 1 = 32
N = 32 ways
Using the combination formula, it is found that the officers can be sent in 32 ways.
The order in which the officers are called is not important, hence, the combination formula is used to solve this question.
Combination formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
0 officers:
[tex]C_{5,0} = \frac{5!}{0!5!} = 1[/tex]
1 officer:
[tex]C_{5,1} = \frac{5!}{1!4!} = 5[/tex]
2 officers:
[tex]C_{5,2} = \frac{5!}{2!3!} = 10[/tex]
3 officers:
[tex]C_{5,3} = \frac{5!}{3!2!} = 10[/tex]
4 officers:
[tex]C_{5,4} = \frac{5!}{4!1!} = 5[/tex]
5 officers:
[tex]C_{5,5} = \frac{5!}{5!0!} = 1[/tex]
In total:
[tex]T = 2(1 + 5 + 10) = 32[/tex]
The officers can be dispatched in 32 ways.
A similar problem is given at https://brainly.com/question/24437717
