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 are from town B. I know this is a combination but I am having a hard time figuring out the answer.

To find the probability of selecting 3 people from town A and 2 people from town B, we need to consider the total number of ways this combination can occur and compare it to the total number of possible council compositions.

First, we need to calculate the total number of ways to choose 5 people from the total 8 from town A and 7 from town B. This is a combination problem, expressed as "8 choose 3" for town A and "7 choose 2" for town B. The number of ways to choose 3 people from town A and 2 people from town B can be calculated as follows:

Number of ways = (8 choose 3) * (7 choose 2)

For the combination formula "n choose r," where n represents the total items to choose from and r represents the number of items to choose, it can be calculated as:

n! / (r! * (n-r)!)

For the first part, (8 choose 3), the calculation is:

8! / (3! * (8-3)!) = 56

For the second part, (7 choose 2), the calculation is:

7! / (2! * (7-2)!) = 21

Therefore, the number of ways to choose 3 people from town A and 2 people from town B is:

Number of ways = 56 * 21 = 1176

Now, we need to calculate the total number of ways to choose 5 people from the total number of attendees. There are 8 people from town A, 7 people from town B, and 5 people from town C, totaling 20 people. Therefore, this can be calculated as:

Total number of ways = 20 choose 5

Using the combination formula, the calculation is:

20! / (5! * (20-5)!) = 15,504

Finally, to find the probability, we divide the number of desired outcomes (1176) by the total number of possible outcomes (15,504):

Probability = Number of ways / Total number of ways = 1176 / 15,504 = 0.0758 (rounded to four decimal places)

So, the probability that 3 people are from town A and 2 people are from town B in the randomly selected council of 5 people is approximately 0.0758.

[(8 combination 3)(7 combination 2)(5 combination 0)] divided by (20 combination 5)

= .0758513932