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at the first tri city meeting where 8 people are from twon A 7 people are from town B and 5 people are from town C. If the council consists of 5 people find the probability that 3 people are from town A and 2 people are from town B. How do i do this

User Icon for Step-by-Step Bot Step-by-Step Bot answered
1 year ago

To find the probability that 3 people are from Town A and 2 people are from Town B, we can follow these steps:

Step 1: Calculate the total number of ways to select 5 people from the total of 8 people from Town A, 7 people from Town B, and 5 people from Town C. This can be done using combinations:

C(8, 3) * C(7, 2) * C(5, 0) = (8! / (3!(8-3)!)) * (7! / (2!(7-2)!)) * (5! / (0!(5-0)!))

Step 2: Calculate the total number of ways to select any 5 people from the total 20 attendees (8 from Town A, 7 from Town B, and 5 from Town C):

C(20, 5) = 20! / (5! * (20-5)!)

Step 3: Divide the number of ways to select 3 people from Town A and 2 people from Town B by the total number of ways to select any 5 people from the total attendees:

P = (C(8, 3) * C(7, 2) * C(5, 0)) / C(20, 5)

Now you can substitute the values and calculate the probability P.

User Icon for Explain Bot Explain Bot answered
1 year ago

To find the probability of this event, we need to consider the total number of ways the council can be formed and the favorable outcomes where 3 people are from town A and 2 people are from town B.

First, let's calculate the total number of ways the council can be formed. Since there are 8 people from town A, 7 people from town B, and 5 people from town C, we have a total of 8 + 7 + 5 = 20 people to choose from to form the council.

The number of ways to choose 5 people out of 20 can be calculated using the combination formula, also known as "nCr". The formula is:

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

where n represents the total number of items to choose from, and r represents the number of items we want to choose.

Using this formula, we can calculate the total number of ways to choose 5 people out of 20:

Total number of ways = 20! / (5! * (20 - 5)!) = 20! / (5! * 15!)

Now, let's consider the favorable outcomes where 3 people are from town A and 2 people are from town B. We need to multiply the number of ways to choose 3 people from town A with the number of ways to choose 2 people from town B:

Number of favorable outcomes = (8! / (3! * (8 - 3)!) * (7! / (2! * (7 - 2)!)

Finally, we can calculate the probability of this event by dividing the number of favorable outcomes by the total number of ways:

Probability = Number of favorable outcomes / Total number of ways

Now, you can plug in the values in the formulas and simplify to find the actual probability.