##### Inhomogeneous Product Structure
eshiar
For today's lecture (1/14/15), regarding the example with the different ways you can plan your M-F week, I'm a bit confused as to why Monday has 3 possibilities instead of 4. I know it's dependent on Tuesday's activity since the same activity cannot be done in consecutive days, but since it is the first day of the week, aren't we allowed to choose any of the four activities to do? Can someone please explain this to me? Thanks in advance!
ccollet: Jan. 14, 2015, 10:58 p.m.
Monday is the first day of the week, however, we planned the week in class according to Wednesday. When you choose to tan on Wednesday, there are three options for Tuesday (snorkeling, horseback riding, or sailing) since you wouldn’t have been able to tan and also three options for Monday since you would not be able to do one of the options for Tuesday. There are three options for both Tuesday and Monday again when you have three options for Wednesday (if you don’t tan Wednesday) for the same reason. I guess try not to think of the week chronologically and instead base the week on the condition for Wednesday. Hopefully that helps!
weisbart: Jan. 18, 2015, 10:52 p.m.
"I guess try not to think of the week chronologically and instead base the week on the condition for Wednesday."  Exactly! You have it right. You have four options for Monday, however, once you have a choice for Tuesday, you are limited in what you could have chosen for Monday. Now, only three choices are available to you.  You could have chosen Monday first and had four options, but then this makes the problem more complicated because depending on your choice for Monday you will have varying numbers of choices for Tuesday. If Monday and Wednesday are the same, you have three possible choices for Tuesday. If Monday and Wednesday are different, then you have two choices for Tuesday. Rather than deal with this complexity, we choose Tuesday first (3 choices). This then forces exactly there choices for Monday.