MHB How can I find time to study math with a busy schedule and living situation?

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Finding time to study math can be challenging due to a busy schedule and shared living situations. The discussion highlights the difficulty of balancing study time with work and roommate dynamics, particularly with limited personal space. One participant shares their experience of using a college library to review math basics while managing a hectic routine. They express a commitment to deepening their understanding of math despite these obstacles. The conversation emphasizes the importance of personal effort in overcoming study challenges.
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Eight guests have to be seated 4 on each side of a long rectangular table. 2 particular guests desire to on one side of the table and 3 on the other side. The number of ways in which sitting arrangements can be made is

(a) 1732
(b) 1728
(c) 1730
(d) 1278

My Work:8 options for person 1.
3 options for person 2, who wants to be on the same side as person 1. 4 options for person 3, who wants to be on the opposite side. 3 options for person 4, who wants to be with person 3. 2 options for person 5, who also wants to be with person 3. 3 options for person 6. 2 options for person 7. 1 option for person 8.

8 * 3 * 4 * 3 * 2 * 3 * 2 * 1 = 3456 ways

Is this right? It is not among the choice answers.
 
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Let's look at the two people being on one side and the three being on the other. We have:

$$(4\cdot3)(4\cdot3\cdot2)3!=1728$$

Ways to seat them. However, it we reverse the sides that the two groups are seated, we must double this number to 3456. Since 3456 isn't an option, then I would interpret the problem to mean that the two groups who are to be seated on the same side with each other, have particular sides they desire. :)
 
MarkFL said:
Let's look at the two people being on one side and the three being on the other. We have:

$$(4\cdot3)(4\cdot3\cdot2)3!=1728$$

Ways to seat them. However, it we reverse the sides that the two groups are seated, we must double this number to 3456. Since 3456 isn't an option, then I would interpret the problem to mean that the two groups who are to be seated on the same side with each other, have particular sides they desire. :)

You are way too smart. I'll never catch up to your knowkedge of math.
 
RTCNTC said:
You are way too smart. I'll never catch up to your knowkedge of math.

As long as you are personally working to deepen your understanding, then when that happens, I would take that as a personal victory. :)
 
MarkFL said:
As long as you are personally working to deepen your understanding, then when that happens, I would take that as a personal victory. :)

The following is not an excuse. I have a split days off schedule. I am off on Tuesday and Friday. You have no idea how hard it is for me to find time for math on such a crazy schedule.

I also do not live alone. I share an apartment with two roommates to help pay the rent, gas, etc. I hardly have the apartment to myself. My roommates and I have different work schedules but there are days when at least one of them has the same day off I have, you see?

I have a Lehman College alumni ID card that I sometimes use to visit the campus library. It feels a bit odd being in the library at a college I graduated from in 1994. Undetstand? I do my best to review math basics and learn new material.

This LaTex stuff takes time to learn well. I hope you now have a better understanding of my situation. Let me also say that my cell phone is my laptop, computer, tv, tablet, etc. Not excuses but reality, my reality.
 
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