[Discrete Mathematics] Permutations and Combinations Examples 2

In this video we do a letter permutation problem, a random walk problem, and a circular table problem.

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Hello, welcome to TheTrevTutor. I'm here to help you learn your college courses in an easy, efficient manner. If you like what you see, feel free to subscribe and follow me for updates. If you have any questions, leave them below. I try to answer as many questions as possible. If something isn't quite clear or needs more explanation, I can easily make additional videos to satisfy your need for knowledge and understanding.

[KoGaVipraTajGaLipa]

Thank you for your videos, really helpful with getting back into Discrete Math after a 15-year break. I have found an easier way to think about the circular tables problem, at least for me. So we have 16 people to arrange, and let us assume we have 16 total chairs we need to fill in. We can find the number of arrangements by a simple 16 * 15 * 14 * ... * 2 * 1 which is 16! and all we need to do is to divide that number by 10 for the possible number of the around the table rotations (non-new arrangements) of the first table and by 6 for the possible number of the around the table rotations (non-new arrangements) of the second table. So the TOTAL would be equal to 16! / 10 * 6 which is basically a bit more simplified version of your answer.

[travelsonic]

I should have started watching this series back when my semester began, it makes things a lot clearer... probably mainly because it isn't like the class I am taking, where everything is crammed into 1-a-week 3 hour classes that take place at night. ~_~ FML

[jessstuart]

It doesn't matter which table you choose first because C(16, 10)=C(16, 6). This works for any two numbers N and M where they sum to the top number in the binomial. C(M+N, N)=C(M+N, M).

If CW and CCW directions are not important, you need to divide your answer by 4.

[matthewsattam]

Hi Trev, love your videos! One thing I always get confused about is when to multiply vs. add. In your last problem when I tried it on my own before you showed the answer, I added the 3 expressions when they should have been multiplied. For your last problem in the "Permutation Practice" video, we added up all of the cases. Just curious if there is an intuitive way to think about when to multiply vs when to add? You are the best.

[TOA]

First of all, thanks. Your videos are super helpful, as always. I have one question about the circular table exercise. My initial approach was slightly different. I am getting a different answer, and I am trying to figure out why. My train of thought is: I start sitting people at table A (10 seats), one by one. Then, I proceed to table B (6 seats). So, let's start. For the first table, I can sit people in 1 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 ways. Continuing with the second table, that is, 1 x 5 x 4 x 3 x 2 x 1. After simplifying, that is (15!/6!) x 5! which gives an answer smaller than yours. I understand that I am missing cases but I don't know which ones. Any idea what I am missing here? Thanks! 🙂

[davidislam]

How do you know when to multiply or add? For instance, in the last question I thought of adding the two combinations.

[II_xD_II]

in those graphical questions, we can use manhattan distance to find the path

[waihan]

For two tables question, it can also be considered as (16 * 15 * 14 * ... * 6)/10 * (6!/6)

[tennisswimmingrugby]

Trev can you upload a counting #of passwords video from easy to difficult

[eimaldorani]

@03:05 (or as u said ) since in each step we should move either one step to the right or one to the up, then it means must be arranged in allternative, i.e URURURURU, ISN'T IT!?

WHICH MEANS 5!X4!

[arib]

In the question "(-1, 0, 6) -> (3, 2, 8) where x -> x+1, y->y+1 or z ->z+1 in each step" dont you need to change out "or" with "xor"? If not we dont specify only 1 movement each step? With or you could go both in x and y at the same time, right?... Or am I misunderstanding something?

[grafficconcepts]

In the two circular tables question, if the question says "how many ways can we sit 16 people around two circular tables" wouldn't this mean that you would have to account for people changing tables (ie. in one arrangement person x could be on the 10 seater and an another arrangement person x could be on the 6 seater)? Or am I missing where this has already been taken into account?

[张永成-pj]

i can't understand in circular table's question why we rotate everyone one position it need divide the number of total people

[marionejenkinson]

In the how many permutations question. Shouldnt it be 1 x 3 x 5 ... because 4 letters is already used. So 9 - 4 used = 5. Or if j can be used again it should be 1 x 3 x 6 ... because 9 - 3 = 6. Please explain

[rimibiswas]

I believe you could have also done 16P10/10( how many ways to arrange 10 people out of 16 at the first table) and then 6P6/6(how many ways to arrange 6 people out of the number of people left(16-10=6)) and then multiplied it like you did. Is that an ok way to think of the problem?

[moolikethecow]

I am a little confused for question 1 part 3. "How many cons, vowel, cons words can be made." Isn't this question similar to the problem in your last video where you were inserting different letters into TALLAHASSEE? When I did this problem before you explained it, I did (3!) for the order of the vowels, multiplied by, (5 choose 3) since there are only 5 positions where there can be cons | vowel | cons and 3 potential vowels, and then multiplied by (6!) for the order of the consonants. Yet that is completely wrong. Could you please explain this further? Thanks

[eimaldorani]

@05:40 How many ways can we sit 16 people around two circular tables, one holds 10 and another holds 6 seats!?

I'm afraid that your answer is not correct, becuase we can start we the smaller table too, isn't it?
starting with big table or small table= ur answer+....

[jerrychen]

hi, I have question 2:37 if I change Q3 a bit => how many words can be made that contain ConsVowelCons?
Is the answer 3!*C(4, 4)*4!*C(4, 2)*2! ?
My thought was place the three vowels first, then chose four Cons fill the interval blank, at last fill the remain Cons in the interval.
Am I correct or not?

[jeff_kola]

Hi I don't understand how you know when to use the division rule?

[bugrahandurukan]

i didnt understand how we approach the questions