Final answer:
The dispatcher has 32 options for dispatching police cars when considering the number of cars sent and their state upon arrival at the scene. The total number of options is calculated by counting combinations for sending different numbers of cars and multiplying by the two different states each option can have (sent or not available after arrival).
Step-by-step explanation:
The question involves determining the number of options a radio dispatcher has for sending police cars to the scene of a situation. As the dispatcher has the choice to send no cars, one car, two cars, three cars, or all four cars, we can calculate the number of options using combinatorics, specifically counting the number of combinations in each case and summing them up.
Here are the options:
- No cars sent: 1 way
- One car sent: 4 combinations (because there are 4 cars to choose from)
- Two cars sent: 6 combinations (4 choose 2)
- Three cars sent: 4 combinations (4 choose 3)
- All four cars sent: 1 way
To find the total number of options, we add up all the ways the dispatcher can send the cars:
1 + 4 + 6 + 4 + 1 = 16 options
However, for each of these options, the sent cars can also have two states: available or not available after reaching the scene. Therefore, we must consider these states for every option. If we assign 2 states to each of the 16 options, the total number of different scenarios is 16 x 2 = 32.
Thus, the radio dispatcher has 32 options for sending the police cars to the scene.