To find the probability that 3 people are from town A and 2 people are from town B in a council of 5 people, we can use combinations.
Step 1: Calculate the total number of ways to choose 5 people from the total available population.
The total available population is 8 + 7 + 5 = 20 people.
So, the total number of ways to choose 5 people from a population of 20 is given by the combination formula: C(20, 5) = 20! / (5! * (20-5)! ) = 15504.
Step 2: Calculate the number of ways to choose 3 people from town A.
The number of ways to choose 3 people from town A is given by C(8, 3) = 8! / (3! * (8-3)! ) = 56.
Step 3: Calculate the number of ways to choose 2 people from town B.
The number of ways to choose 2 people from town B is given by C(7, 2) = 7! / (2! * (7-2)! ) = 21.
Step 4: Multiply the number of ways to choose 3 people from town A by the number of ways to choose 2 people from town B to get the desired outcome.
56 * 21 = 1176.
Step 5: Calculate the probability by dividing the desired outcome by the total number of possibilities.
Probability = Desired Outcome / Total Number of Possibilities = 1176 / 15504 ≈ 0.07576.
Therefore, the probability that 3 people are from town A and 2 people are from town B in a council of 5 people is approximately 0.07576 or 7.576%.