Question

college visits alex runde is a high school student who lives in bradenton, fl, and he wishes to visit colleges in the following cities: st. cloud, mn; valparaiso, in; lindonville, vt; asheville, nc; and norman, ok. in how many different ways can alex visit each of these cities and return home to bradenton?

Answer 1

Alex can visit each of the cities and return home to Bradenton in 60 different ways. To find the number of different ways Alex can visit each of these cities and return home to Bradenton, we need to calculate the number of permutations.

Step-by-step explanation:

To find the number of different ways Alex can visit each of these cities and return home to Bradenton, we need to calculate the number of permutations. Since he needs to visit each city and return home, we can think of this as arranging the cities in a specific order.

• Step 1: Calculate the number of ways to arrange the cities. There are 5 cities, so there are 5! (5 factorial) ways to arrange them. This is equal to 5 x 4 x 3 x 2 x 1 = 120.
• Step 2: Since Alex needs to return home after visiting the cities, we don't need to consider the order of the return trip. So, we divide the total number of arrangements by 2.
• Step 3: Calculate the final result by dividing the number of arrangements by 2: 120 / 2 = 60.

Therefore, Alex can visit each of the cities and return home to Bradenton in 60 different ways.