A candidate for office plans to visit 6 cities before the state primary.
How many different ways can the campaign staff arrange her travel route?
To calculate the number of different ways to arrange the candidate's travel route, we need to find the number of permutations.
We have 6 cities to visit, which means there are 6 options for the first city, 5 options for the second city, 4 options for the third city, and so on, until only 1 option is left for the last city.
So, the number of different ways to arrange the travel route can be found by multiplying these options together:
6 × 5 × 4 × 3 × 2 × 1 = 720
Therefore, the campaign staff can arrange the candidate's travel route in 720 different ways.
To find the number of different ways the campaign staff can arrange the candidate's travel route, we can use the concept of permutations.
Since there are 6 cities to visit, the candidate can start her travel route from any of these cities. Let's represent the cities by the letters A, B, C, D, E, and F.
The first city can be chosen in 6 different ways. Once the first city is chosen, the second city can be chosen from the remaining 5 cities in 5 different ways. Similarly, the third city can be chosen from the remaining 4 cities in 4 different ways, and so on.
Therefore, the total number of different ways to arrange the candidate's travel route is calculated as:
6 * 5 * 4 * 3 * 2 * 1 = 720
So, there are 720 different ways the campaign staff can arrange the candidate's travel route.