a tourist in framce wasnts to visit 5 different cities. if the route is ransomly selested what is the probability that she will visit ciites in alphabetical order
To calculate the probability, we need to determine the total number of possible routes and the number of routes that satisfy the condition of visiting cities in alphabetical order.
The total number of possible routes can be found using the concept of permutations. Since the tourist wants to visit 5 different cities, the number of possible routes can be calculated as 5 factorial (denoted as 5!).
5! = 5 x 4 x 3 x 2 x 1 = 120
Now, we need to determine the number of routes that satisfy the condition of visiting cities in alphabetical order. In this case, visiting cities in alphabetical order means that the cities must appear in the order of A, B, C, D, E.
However, since the route is randomly selected, there is only one specific order that satisfies this condition. Therefore, the number of routes that satisfy the condition is 1.
Now, we can calculate the probability by dividing the number of favorable outcomes (1) by the total number of possible outcomes (120).
Probability = Favorable outcomes / Total outcomes
Probability = 1 / 120
So the probability that the tourist will visit cities in alphabetical order is 1/120 or approximately 0.0083 (rounded to four decimal places).