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

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mathdad
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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.