Discrete Math II - 6.5.1 Combinations with Repetition

We begin the final section of Chapter 6 by examining what happens when we have a combination, but repeated values are allowed. You will notice that I use a notation that isn't included in the textbook. It is standard notation for the combinations with repetition model. We also take our first look at the linear equations model, which we will revisit often in this course.

Video Chapters:
Intro 0:00
Permutations with Repetition (Distinct Objects) 0:08
Combinations with Repetition - Brute Force 1:51
Understanding the Combinations with Repetition Model 4:23
Combinations with Repetition Examples 7:55
Linear Equation Model 10:32
Practice with Linear Equation Model 13:35
Final Practice 16:43
Up Next 18:57

This playlist uses Discrete Mathematics and Its Applications, Rosen 8e

Power Point slide decks to accompany the videos can be found here:

The entire playlist can be found here:

[perseusgeorgiadis]

First person I've seen talk about combinations with repetitions on YouTube. This series really is a gold mine for probability/statistics students

[maddie]

Thank you for teaching in such a digestible and concise way!

[gottadomor]

A timely lesson, t/y.
I'm being driven bonkers trying to figure out how many combinations there are rolling 5 dice.
By hand - brute force as you say - calc'd the combos for 2 dice thrown, and 21 jibes w/ the vid's.
Had never seen the "n + k - 1 over k" terminology before so this much appreciated. Never saw that during my permutations & combinations class (or at least don't remember (long ago tho now.)) T/y again.

[FlowersAndPhilosophy]

It's been 5 hours. Now I've solved my problem and can sleep. Thank you :)

[Monsta]

Thank you for helping me pass discrete math 1 and now discrete math 2 <3

[davidstone]

Great explanation of the linear model -- very cool. I also loved the illustration of how the dividers among the buckets (in the pennies problem) count as items in the same way that the pennies do; that explains where the "7" came from (5+3-1). As for the integers problem, does 'integers' generally mean 'positive whole numbers'? I've generally been told to think of integers as both + and -. A smart-aleck student could, in that case, say that there are infinite ways to add three integers to get a sum of 7.

[GenJoseGhost]

In minute 6:04 you state that you are going to find all the COMBINATIONS of 7 total objects, however, shouldn't it be all permutations with repeated elements?

[Reverb]

Please I do not understand where the 2 dividers come from (PS. I unknowingly choose Discrete Maths as my first ever college level math class please bear with me)

[SuperRockcore]

“Order” is a bit confusing here isn’t it?

[thomson]

how come 5 identical pennies can be in order? it's confusing. i think when they become not identical. how comes 3 different bucket choose 5 pennies? usually people think put pennies in bucket. making mathematic sense but no real life sense

[Auroralalabu]

10:15
But don't we also need to consider the combination of 3, as we assign 3 to 3 children but they can be assigned any one of those, so I thought the answer would be (3, 3) x ((3, 2))