Classroom seating arrangement problem. [Combinatorics]

I’m a high school teacher and I’m doubting myself with this one.

I have nine groups of tables in my classroom and 34 students total. There is currently one group of five, six groups of four, A group of three and a group of two. I want the students to rearrange themselves so that they are all at a different table and they are sitting with all new students. How many possible combinations of student arrangements are there?

My thinking goes like this: The group of 5 has 8x7x6x5x4=6720 possibilities, six groups of four have 6x8x7x6x5=10080 possibilities, the groups of three and two have 8x7x6=336 and 8×7=56 possibilities, respectively. So we’re looking at a total of 17192 possible seating combinations.

Am I on the right track here? I feel like I’m missing something but I’m not sure what it is.

submitted by Nevin Manimala Nevin Manimala /u/RadDudeGuyDude
[link] [comments]

I remember learning a trick in high school to add all numbers in a sequence and have forgotten what it’s called.

For example adding up all the numbers between say 5 and 35. Instead of having to add 5+6+7+8… there was a way to add them all by some equation. Please help.

submitted by Nevin Manimala Nevin Manimala /u/tollsworth
[link] [comments]

How do I get started on Quantum Mechanics?

So I’ve recently gotten interested in QM, thanks to some discussions on this sub. Problem is, I have almost no experience in physics. Forget QM or general relativity, I barely know anything about classical mechanics. That said I do have some background in maths. Would it be possible to start immediately on QM without background in classical physics?

My relevant math background includes analysis and algebra and the first year graduate level, basis functional analysis, measure-theoretic probability theory, linear algebra, topology and complex analysis.

What book would you recommend for someone of my background? Preferably I’d like it to be fully mathematically rigorous, but some intuitive explanation alongside the rigour might also be nice.

Thanks in advance!

submitted by Nevin Manimala Nevin Manimala /u/WaltWhit3
[link] [comments]

What do you think is the next car brand to bite the dust in the US market?

Please try to qualify your comment instead of just naming a brand. I don’t think the actual FIAT brand has a future in this country. Marchionne was first to the sedan slaughter by killing off the 200 and Dart, and I think the 500 is close behind. Maybe it had some hope of becoming an EV-only brand, but his disdain for the 500e and recent comments about FIAT falling into irrelevancy in Europe makes me think it’s going to be fully refocused into an emerging markets brand a la Datsun.

Hard Mode: Pick the next luxury brand to go defunct.

submitted by Nevin Manimala Nevin Manimala /u/argent_pixel
[link] [comments]