One out of 7! = 1/(7*6*5*4*3*2*1)
= 1/5040
= 1/5040
Yes I am positive. Your chances are 1 in 7 of getting the correct (first in alphabet) city first. Then you still have six others to worry about.
If a student is chosen at random, find the probability of getting someone who is a man or a non-smoker. Round your answer to three decimal places.
********non***regular heavy total
man*****135*****64******5*****204
women***187****21*******9*****217
total***322****85*******14****421
Answer in decimal (round to nearest 3)
Please help me, I've taken more than an hour to figure this problem out! Please guys! Really appreciate it. Sorry for the stars, I had to make the chart so that it corresponds with the correct data!
Since there are seven cities to visit, there are 7! (7 factorial) possible routes in total. This means that there are 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5040 different routes.
Now, let's determine the number of routes that satisfy the condition of alphabetical order. Imagine numbering the cities from 1 to 7 in alphabetical order. The tourist must visit each city in ascending numerical order. For example, if the tourist visits city 3, they must have already visited cities 1 and 2.
Since the cities must be visited in alphabetical order, we can consider each city as an independent event with only 2 possible outcomes: visited before or visited after all the cities that come later in alphabetical order.
For example, for city 1, there are 6 cities that come after it in alphabetical order. The tourist must visit city 1 before visiting any of those 6 cities.
Similarly, for city 2, there are 5 cities that come after it in alphabetical order. The tourist must visit city 2 before visiting any of those 5 cities.
Using this logic, we can determine the number of routes that satisfy the condition of alphabetical order as:
1 * 1 * 2 * 3 * 4 * 5 * 6 = 720
Therefore, the probability that the tourist will visit the cities in alphabetical order is given by:
Number of favorable outcomes / Total number of possible outcomes
Probability = 720 / 5040 = 1 / 7
Hence, the probability that the tourist will visit the cities in alphabetical order is 1/7 or approximately 0.1429.