PERMUTATIONS and COMBINATIONS Review - Discrete Mathematics

Welcome to Discrete Math 2! The course topics are introduced right at the beginning. In this video, we review permutations, combinations, permutations with repetition, and combinations with repetition. If any of these topics are unclear, please refer to the Discrete Math 1 videos I have uploaded on the channel, or leave a comment below!

#DiscreteMath #Counting #Mathematics #Permutations #Combinations

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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.

[albik]

this was in the comments and went unanswered once... at 21:01, no container can be nonempty, there must be at least one ball in each container, leaving 4 balls to be placed in the four containers ==> the equation should be x_1+x_2+x_3+x_4=4 ==> I count( 4+4-1 choose 4) = (7choose4)

[NewtonCazzaro]

THANK YOU SO MUCH!!! YOU ARE THE BEST, PLEASE DO NEVER STOP TO MAKE VIDEOS ON MATH - ENGINEERING/CS CLASSES.

YOU ARE THE EBST!

[combativegraduate]

You are actually god sent, I have watched about 70 of your videos in 3 days preparing for an exam, and it has been an absolute pleasure. Thank you.

[anitpeter]

@21:00 its wrong..its given none are empty so x>=1

[legume-dczx]

at 19:12, the primes need to be on the other side of the equation: x1 = x1' + 2, x2 = x2' + 2, ... etc. The point is that you're *factoring out* the minimum values of each variable to distinguish the number of degrees of freedom you actually have when assigning values.

[srarun]

How are there 14 spots? I see only 13!

*1* _X1_ *2* _X2_ *3* _X3_ *4* _X4_ *5* _X5_ *6* _X6_ *7* _X7_ *8* _X8_ *9* _X9_ *10* _X10_ *11* _X11_ *12* _X12_ *13*

How ever there will be 14 spots if there are 13X s, since x can also be 0

[joeljoseph]

For the Student answering questions problem part c: is it possible to answer 6 choose 4 times 6 choose 3 or is that wrong?

[miksurankaviita]

At 13:30, you could have done it the way you started doing it. i=4 and then i+4 would just be i and i+3 would be 7-i ....

[davidjohnson-mysr]

21:10. No container empty means no container has zero balls. The answer is 7 choose 3.

[sadaf]

Hey Trev
in 12:00 part c, how is this wrong
(6 choose 4)*(6 choose 3), I saw your reply below on the same, but that didnt explain it explicitly.
Could you please clarify it for me
and thanks for this amazing charity for humanity, I live in a warzone educating myself where my schools are shut down.I promise to pay it back to humanity in any other form.
Thanks again

[mdghazwanahmedkhan]

hi there sir in last question a) nonempty but you are solving for x'i >=0 i.e. bin can take 0 balls which as per question should not be, please explain why you did so?

[manic]

21:10 x has to be greater or equal to 1

[nicolebilaw]

Shouldn't you be adding 6 instead of subtracting 6 to 12 at 19:35?

[jasona]

Thanks for posting this Trev, you've helped me out so much by doing this tut! I have a final coming up and your study guides really gave me an outline of what to study. Keep up the great work!

[siline]

You have such beautiful laugh 10:43 😫😫
I really love you
You saved

[DiegoSalazar-ufjs]

Thanks so much for posting. But I have one question about the integer solutions. You say that there are 14 spots but I only count 13. What am I missing? I think spots are the black spaces between the yellow x's and the last two x's on the margins? So I count 11+2.

[-nitishkumar]

Thank you very much for flourishing budding mathematician like me

[ionaiobidze]

Absolutely great video but you got one thing wrong, when you have n amount of objects, you have n + 1 places to chose where to divide this n number ob objects. not n + 2.

[shaun_vermaak]

I don't get your statement of picking 14 spot and picking 2 of them. There are 13 spots. I understand the stars and bars methods that comes after that

[LisiQarkaxhija]

Can you post anything about Axiom of Choice and how to use it in examples? Thank you for your videos!