The Combination Formula and Why it Works | Combinatorics, Combinations and Permutations
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- čas přidán 22. 08. 2024
- How many ways can we select k objects from a collection of n objects? The number of combinations of k objects from a collection of n objects has a very nice formula that we will demonstrate and explain in today's video combinatorics lesson!
I assume you're mostly familiar with factorials and permutations in this lesson, if you need to brush up on either topic, check out these lessons!
Factorials Lesson: • What is That Exclamati...
Permutations Lesson: • The Permutation Formul...
The combination formula is also called a binomial coefficient because it appears in the powers of binomials. It's very cool and we'll talk more about that in another lesson!
SOLUTION TO PRACTICE PROBLEM:
How many ways can we select 4 actors from a group of 7? That would be 7 choose 4, which is 7!/((7-4)!*4!) = (7*6*5*4)/4! = 35.
How about 7 choose 3? That is 7!/((7-3)!*3!) = (7*6*5)/3! = 35.
Look at that, they're equal! Why is that? You can think of it like this. The number of ways we can select 4 actors from a group of 7 is the same as the number of ways we can select 3 actors to NOT be chosen for the play. If we choose the actors that won't get roles, we have necessarily chosen the remaining actors to get roles as well. Another example is that 8 choose 2 is equal to 8 choose 6. If we select 2 objects from a group of 8, we have in a way also chosen the other 6 to not be selected. So the number of ways of choosing 2 objects from 8 is the same as the number of ways of choosing 6 from 8! Can you generalize this principle?
I hope you find this video helpful, and be sure to ask any questions down in the comments!
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Had such a hard time intuitively conceptualizing this. This is the first video that explained it in a way that made sense!
So glad to hear it, thanks for watching!
I agree. I looked at some other videos but this one explained the formula properly. Thank you.
Thank you so much. It took me a few watches, but I understand this concept soooo much better now.
So glad it helped, thanks for watching and let me know if you ever have any questions!
This is the most helpful video I have found on the subject. Thank you
Glad to hear it, thanks for watching! If you're in the mood for some tunes, check out my new math song that came out today! czcams.com/video/0Oro28Xkzbg/video.html
Thank you for this video! I was thinking about this but I wasnt sure It was right but with your video I was able to confirm my thought process. Thank you again :D
Glad it was helpful!
This actually helped me grasp the concept really well thanks
Glad to hear it - thanks for watching!
you really need to teach my teacher how to teach, Thanks a lot
As a 3rd year CS student; My High School teacher could have just linked me to this video from the future and would have saved me years of not being piss scared of Permutations and Combinations cause they didn't make any sense
dear teacher, thanks for the demo, your choice for both n and k being actors made it little confusing and a bit hard to follow
Finally I understand how combination formula works. Thank you so much
So glad it helped, thanks for watching! Let me know if you ever have any video requests!
@@WrathofMath I have one video request. Can you do a video on how to calculate frequency and probability of 5 poker hands and cover cases like full house,royal flush, straight flush,flush, straight, three of a kind. I'm not sure if this is already on the channel. If not it would be really helpful if you do a video on this.
Amazing. You earned a subscriber man
Glad it helped and thanks for subscribing! Let me know if you ever have any questions!
Sir, can you please help me solve a problem? It's stated below:
Six different toys and five identical balloons are all handed out to a group of four children. What is the number of possible distributiona if every child gets at least one toy?
Bijection helps
When you sucked/suck (suck meaning slow) at this topic in math but are still persistent. Replay, replay, replay until it makes sense. It's required to understand the hypergeometric distribution. Thank you sincerely for this video.
great explanation
The thumbnail should have a k! on the bottom instead of n!
subscribed. could you please do some videos on linear algebra? edit: nevermind
Thanks for watching and subscribing! I have some linear algebra videos, which is maybe why you said never mind, but let me know if you have any specific requests!
viva mrs boose!
Great video man!, btw your thumbnail is wrong 😅
cool video, you deserve more views!
Thanks Mauro! If you know anyone who would find the lessons helpful, sharing them is really appreciated. Let me know if you ever have any video requests and Happy New Year!
Amazing tysm
Thank you!
My pleasure, thanks for watching!
bro cooked with this proof
thank u so much
My pleasure, thanks for watching!
20 yrs old I I finally understood this formula
Better late than never - thanks for watching!
factrolial means ?????
Here's my video on the topic, though it's really old so it might suck: czcams.com/video/5ne2xBWhdJ4/video.html
5! = 5*4*3*2*1
7! = 7*6*5*4*3*2*1
and so on
Gah
Thanks for watching, do you have any questions I can help answer?
Nope! But thank you for the video!
u might want to change the thumbnail, since the formula in it is wrong
Your thumbnail has a n! Instead of a k!. Fix it.