At the first tri-city meeting there are 8 people from town A, 7 people from town b and 5 people from town c. If a council consisting of 5 people is randomly selected, find the probability that 3 are from town A and 2 from town b.
I know that the probability for town A is 3/8 and for town B it is 2/7
how do I figure out that the answer is either of these?
a.23/1000
b. 9/150
c. 9/125
d. 49/6460
To find the probability that 3 people are from town A and 2 people are from town B, you can use the concept of combinations.
First, calculate the total number of ways to select 5 people from the total number of attendees, which is (8+7+5) = 20. This can be represented as C(20, 5) or 20 choose 5.
The number of ways to select 3 people from town A can be calculated as C(8, 3) or 8 choose 3, which is the number of combinations of 3 people from town A out of the total 8 people from town A.
Similarly, the number of ways to select 2 people from town B is C(7, 2) or 7 choose 2, which is the number of combinations of 2 people from town B out of the total 7 people from town B.
To calculate the probability, divide the number of favorable outcomes (selecting 3 people from town A and 2 people from town B) by the total number of outcomes (selecting 5 people overall).
The probability can be calculated as:
Probability = (Number of ways to select 3 people from town A) * (Number of ways to select 2 people from town B) / (Total number of ways to select 5 people)
Probability = C(8, 3) * C(7, 2) / C(20, 5)
Now, let's calculate the probability and see which answer choice matches:
Probability = (8C3 * 7C2) / (20C5)
To calculate this, we can use a calculator or mathematical software. The answer should be in fraction form.
After calculating the probability, we can see that the correct answer is c. 9/125.