I do not understand how to work this problem out. I have a series of other questions that are similar, and it would really help me out if someone could help me understand how to work this problem.
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 answered this same question for you in
http://www.jiskha.com/display.cgi?id=1260061099
I was using standard notation and methods for this type of problem.
What part of it don't you understand ?
To find the probability that 3 people are from town A and 2 people are from town B, we need to understand the total number of possible outcomes and the number of favorable outcomes.
First, let's calculate the total number of possible outcomes. Since we are selecting 5 people from a total of 8 people from town A, 7 people from town B, and 5 people from town C, the total number of possible outcomes is given by the combination formula:
Total possible outcomes = C(8, 3) * C(7, 2) * C(5, 0) = (8! / (3! * (8-3)!) ) * (7! / (2! * (7-2)!) ) * (5! / (0! * (5-0)!) )
Simplifying the above expression, we get:
Total possible outcomes = (8! / (3! * 5!) ) * (7! / (2! * 5!) ) * (5! / (0! * 5!) )
= (8 * 7 * 6 / (3 * 2 * 1) ) * (7 * 6 / (2 * 1) ) * (5 * 4 * 3 * 2 * 1 / (1) )
= ( 56 ) * ( 21 ) * ( 120 )
= 129,0240
Now, let's calculate the number of favorable outcomes, i.e., the number of ways in which we can select 3 people from town A and 2 people from town B. This can be done by finding the combination of 3 people from town A and 2 people from town B:
Favorable outcomes = C(8, 3) * C(7, 2) = (8! / (3! * (8-3)!) ) * (7! / (2! * (7-2)!) )
Simplifying the above expression, we get:
Favorable outcomes = (8 * 7 * 6 / (3 * 2 * 1) ) * (7 * 6 / (2 * 1) )
= ( 56 ) * ( 21 )
= 1,176
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Favorable outcomes / Total possible outcomes
= 1,176 / 129,0240
So the probability that 3 people are from town A and 2 people are from town B is approximately 0.0091 or 0.91%.