Of the 15 teams in the National Hockey League Eastern Conference, three of them are based in canadian cities. Each year, eight of these teams qualify for the playoffs. Assuming that all the 15 teams have an equal chance of getting into the playoffs, what is the probability that
a) none of the canadian teams make the playoffs
b) at least one of the canadian teams makes the playoffs
c) all three canadian teams make the playoffs.
**if i even get hints or help with one part i am sure i can figure it out. thanks.
To solve this problem, we can use the concept of combinations. Let's break it down step by step:
Step 1: Calculate the total number of possible combinations for the 15 teams.
Since there are 15 teams and 8 spots available, we can calculate this using the combination formula:
C(n, r) = n! / (r! * (n-r)!)
Where n is the total number of teams (15) and r is the number of teams that qualify for the playoffs (8).
C(15, 8) = 15! / (8! * (15-8)!) = 6435
So, there are a total of 6435 possible combinations.
Now, let's move on to each scenario:
a) None of the canadian teams make the playoffs.
To calculate this, we need to find the number of combinations where all three canadian teams do not make the playoffs. Since there are 3 canadian teams, we should subtract them from the total number of teams.
Total teams - Canadian teams = 15 - 3 = 12 teams
Number of combinations = C(12, 8)
b) At least one of the canadian teams makes the playoffs.
To calculate this, we need to find the total number of combinations where any one, two, or all three canadian teams make the playoffs. This can be calculated as follows:
Total combinations - Combinations where none of the canadian teams make the playoffs
c) All three canadian teams make the playoffs.
To calculate this, we need to find the number of combinations where all three canadian teams make the playoffs. Since there are 3 canadian teams, we should calculate it as follows:
Number of combinations = C(3, 3)
You can now plug in the values and calculate the probabilities for each scenario using the probability formula:
Probability = Number of desired outcomes / Total number of outcomes
I hope this explanation helps! Let me know if you need further assistance.