Exercise 3.10
How would you determine if you add or multiply the sets of people and set of pills?
RobinJin: Jan. 15, 2015, 3:40 p.m.
I was also confused by this question. In particular, does the question mean that each of the three chosen people will receive all three pills or that each of the three chosen people will each receive one of the three different pills?
weisbart: Jan. 15, 2015, 6:08 p.m.
I could have stated the question a bit better. I'll fix that. In any case, there are only three pills. Each person will get precisely one pill. All choices should be made simultaneously, so there are no issues about the order in which people get things, the only thing that matters is the people and the things they get. Now, I say we can see the problem in a simple way. There are three generations of choice. Each generations of choice represents a different pill. Select a person for each generation of choice you make. This gives that pill to the chosen person. Can anyone finish the problem?
ArieleAndalon: Jan. 17, 2015, 4:20 p.m.
I think I also viewed this problem incorrectly… I saw the first choice as choosing the three people out of thirty, thus 30 x 29 x 28. Then the second choice was choosing the pills, and since there were only three and each person received one pill, that would be 3 x 2 x 1 choices for pills. So basically, I multiplied this all together. Can someone please explain the correct way to solve the problem?
martha2A: Jan. 18, 2015, 10:56 p.m.
Think of it this way: There are three different pills that will be handed out to three individuals in a group of thirty so the first pill has 30 possible individuals to go to while the second pill has 29 possible individuals to go to (excluding the one that already received the first pill). The last pill has 28 possible individuals to go to (excluding the first and second person that received the first and second pill). We multiply 30 by 29 and 28 to get the number of ways in which this experiment can be performed.
weisbart: Jan. 18, 2015, 10:59 p.m.
Exactly! Great job again Martha!
andrearamirez: Jan. 29, 2015, 4:29 p.m.
How do I know I'm choosing them simultaneously and that the order doesn't matter? I saw it as in person #1 getting pill #1, is different from person #1 getting pill #2?
weisbart: Feb. 7, 2015, 11:42 a.m.
You are choosing them simultaneously. The "ordering" here is deciding which pill goes to which person. The pills are named 1, 2, and 3. So the "order" in the generations of choice does not correspond to the order in which the people get the pills, rather it describes which pill goes to which person.