There are 32 teams in the NFL. Sixteen of the teams are in the American Football Conference (AFL) and the other 16 teams are in the National Football Conference (NFC). At the beginning of the season, Julia tried to predict the teams that would be in each conference's championship by randomly drawing 4 teams (2 AFC teams and 2 NFC teams) from a hat. What is the probabliliy that the 4 teams she selected are the same 4 teams that will be in the conferences' championships? Express your answer as a common fraction.
This doesn't make any sense! Please explain!
same question posted by Kate
http://www.jiskha.com/display.cgi?id=1316353131
i still don't understand how you got that
To do these kind of problems, you must have studied the difference between permutations and combinations.
This is a a "combination" type question
You are choosing 2 out of 16 different items in the AFL
that would be C(16,2) = 16!/(14!2!) = 120
You have the same situtation for the other league.
so the number of ways to choose 2 teams from AFL, and 2 teams from NFC
= 120*120=14400
But obviously only one of these will be the correct final selection.
so prob = 1/14400
I really don't know how to explain it in any other way.
I understand your confusion, let me explain the problem step by step.
In the NFL, there are 32 teams divided into two conferences: the American Football Conference (AFC) and the National Football Conference (NFC). Each conference consists of 16 teams.
At the beginning of the season, Julia randomly tries to predict the teams that will be in each conference's championship. To do this, she draws 4 teams from a hat: 2 teams from the AFC and 2 teams from the NFC.
Now, let's calculate the probability that the 4 teams she selected are the same 4 teams that will be in the conferences' championships.
To get the probability, we need to determine the number of favorable outcomes (the 4 teams chosen matching the actual championship teams) and the total number of possible outcomes (all possible combinations of 4 teams).
The number of favorable outcomes is straightforward: since Julia needs to select 2 AFC teams and 2 NFC teams, the total number of outcomes that match the actual championship teams is just 1.
To find the total number of possible outcomes, we need to calculate the number of ways to choose 2 AFC teams out of 16 and 2 NFC teams out of 16.
The number of ways to choose 2 AFC teams out of 16 is given by the combination formula, which is written as "nCk" and calculated as n! / [(n-k)! * k!]. In this case, n = 16 and k = 2. So the number of ways to choose 2 AFC teams is 16C2 = 16! / [(16-2)! * 2!] = 120.
Similarly, the number of ways to choose 2 NFC teams out of 16 is also 120.
To calculate the total number of possible outcomes, we multiply the number of ways to choose AFC teams (120) by the number of ways to choose NFC teams (120). So the total number of possible outcomes is 120 * 120 = 14,400.
Finally, we divide the number of favorable outcomes (1) by the total number of possible outcomes (14,400) to get the probability:
Probability = 1 / 14,400
Therefore, the probability that the 4 teams Julia selected are the exact teams that will be in the conferences' championships is 1/14,400.