Question

A tourist in France wants to visit 4 different cities. How many different routes are possible?

a. 4
b. 6
c. 16
d. 24

Answer 1

To find the number of different routes to visit 4 cities, use the permutation formula 4P4 = 4! / (4 - 4)! The result is 24, meaning there are 24 different routes possible.

Step-by-step explanation:

The number of different routes a tourist in France can take to visit 4 different cities can be calculated using the formula for permutations, since the order in which the cities are visited matters. The formula for finding permutations of n unique items taken r at a time is nPr = n! / (n - r)!. Here, we have 4 different cities, so n = 4 and we want to visit all 4 cities, so r = 4.

The permutation will be calculated as follows:

1. Calculate 4 factorial (4!): 4 x 3 x 2 x 1 = 24
2. Calculate (4 - 4) factorial, which is 0 factorial (0!): 0! = 1 (by definition)
3. Apply the permutation formula: 4P4 = 4! / (4 - 4)! = 24 / 1 = 24

Thus, there are 24 different routes possible for a tourist to visit 4 different cities in France.