A tourist in France wants to visit 5 different cities. If the route is randomly selected, what is the probability that she will visit the cities in alphabetical order?
Answer choice: a)120 b)1/5 c)1/120 d)1/25
So you have 5 possibilities.
The possibility of the first city being letter A is 1 out of 5.
The possibility of the second city being letter B is 1 out of 4.
The possibility of the third city being letter C is 1 out of 3...etc
Thus, we have:
1/5 x 1/4 x 1/3 x 1/2 = 1/120
Easy stuff.
Well, instead of giving you the answer directly, I'll take this opportunity to clown around a bit. Picture this: a tourist in France, hopping from one city to another, trying to visit them all in alphabetical order. Oh là là, the adventure!
Now, let's think about the probability. There are 5 cities to visit, so we can imagine each city as a letter of the alphabet. In order to visit the cities in alphabetical order, she needs to select the cities in the order they appear in the alphabet.
If the route is randomly selected, there is only one correct route that satisfies the condition: starting with the city that comes first in the alphabet, then moving on to the city that comes second, and so on. So, the probability of randomly selecting this specific route is just 1 out of all possible routes.
Now, how many possible routes are there? Well, there are 5 cities to visit, and she needs to visit all of them. That means there are 5! (5 factorial) different ways to arrange the cities.
So, the probability is simply 1 out of 5!, or 1/120. That's option c), my friend!
But hey, remember that in the end, the tourist will have a fantastic time exploring France, no matter what route she takes. The beauty of travel is in the unexpected discoveries along the way!
To calculate the probability of visiting the cities in alphabetical order, we need to determine the total number of possible routes and the number of routes that satisfy the condition.
There are 5 cities to visit, and assuming the tourist visits each city only once, the total number of possible routes can be calculated as the factorial of the number of cities (5!):
Total number of routes = 5! = 5 * 4 * 3 * 2 * 1 = 120
To visit the cities in alphabetical order, there is only one specific order that satisfies the condition: A-B-C-D-E. Therefore, the number of routes that satisfy the condition is 1.
Now we can calculate the probability by dividing the number of routes that satisfy the condition by the total number of possible routes:
Probability = Number of routes that satisfy the condition / Total number of possible routes
Probability = 1 / 120 = 1/120
Therefore, the correct answer is c) 1/120.
To find the probability of visiting the cities in alphabetical order, we first need to determine the total number of possible routes that the tourist can take. Since the tourist wants to visit 5 cities, there are 5! (5 factorial) possible ways to arrange the cities.
Now, let's find the number of arrangements where the cities are listed in alphabetical order. We have 5 cities, so the only way for them to be in alphabetical order is if they are arranged in the order of the English alphabet.
Since the cities need to be visited in alphabetical order, there is only one possible arrangement. Therefore, the number of arrangements where the cities are in alphabetical order is 1.
To find the probability, we divide the number of favorable outcomes (1 in this case) by the total number of possible outcomes (5!).
So the probability is 1/5! (1 divided by 5 factorial).
Simplifying 5!, we get 5 x 4 x 3 x 2 x 1 = 120.
Hence, the correct answer choice is c) 1/120.