Hey Trev... We were introduced to you by our lecturer Dr Morton is S.A. You are so good in explaining.. Do you mind in helping me here; " Qn: How many different 4-digit natural numbers containing only odd digits are there? "
While the licensee plate question is a perfect example part b is worded poorly. I interpreted the problem much differently combining 2 numbers, 1 odd number, 1 even number assuming we had to fit the criteria of a 6 character license plate. In other words, if you have 1 odd number and 1 even number then you already have at least 2 numbers and the same for 2 letters. If you contain at least 2 vowels then you already contain 2 letters. Because of this, my final solution was: 5 * 5 * 5 * 5 * 36 * 36 = 5^4 * 36^2. you have 5 choices of even and odd numbers, 5 choices for a vowel and then you can pick from 10 (numbers) + 26 (letters) 2x (36 * 36).
at around 5:50 with the license plate problem, does the order not matter? Wouldn't it be (5^3)*(26^3)*(# of ways you can mix numbers and letters)? Edit: To be more explicit, on a license plate, wouldn't abc123 be difference from 1a2b3c?
@@Al-nj6ww Why by 6? At first, I thought it should be multiplied by 20 since there are 20 possible permutations for aaabbb (6!/(3!*3!)) But when we have a plate it can be 44bbb4 (20 possible ways to rearrange it to receive a different plate) but it also can be 12abc3 which would mean there are 6!=720 ways to rearrange the symbols and receive a completely different plate. So with each specific plate, we have from 20 to 720 ways to rearrange it. I can't think of a way to have a general calculation considering the order. Either that or the answer given in the video already takes the order into account, since in the last example with plates (c) we apply the rule of product which gives us the same answer as the application of the permutation formula ( P(n,r) = n! ÷ (n-r)! ) would give, meaning that order matters and that abcdef and fedcba are considered to be different plates. Also the application of the permutation formula in the first example would give us 3*4*5*24*25*26 as an answer and the difference between this and 5^3*26^2 is that the second one allows the letters/numbers to repeat. Overall, I think it's a bad example for this topic haha just noticed your comment is 5 years old. well maybe someone else will join the discussion
Sorry, I'm a little confused on the license plate example part b. If we only have six spaces, and one space needs to be an odd (5 options), one space needs to be an even (5 options), another 2 spaces needs to vowels (5x5 options) then we have two spaces remaining, where we could place one letter and one number (10x26) or two numbers (10x10) or two letters(26x26), but I don't understand how we have room for 10x10x26x26 options when only two spaces remain? I was thinking it would be 5^4(26x26) or 5^4(10x26) or 5^4(10x10) depending on how we handled the last two spaces we have remaining after we satisfied odd/even and vowel criteria. Can someone please show me where my intuition is off?
TheTrevTutor thank you, I must have missed the part where you stated this would be an 8 space license plate the first time I watched it. I just went back and rewatched it and now I caught the part where you state that. Sorry my bad
I know this is five months late, but I am going to solve this for anyone who [may] scroll through these comments: If you pick one boy from the possible six, then there will be five possible boys that could pair with him. Moving on to the second boy, there will be four possible pairings with him. (Since the first boy has already been considered). We repeat this process up through boy five, where we get three, two, and one pairing(s) respectively. Note: No pairings are allocated for boy six since all of his pairs have already been listed. Summing the values we have obtained, we get 5+4+3+2+1 = 15 possible pairings of two boys from a group of six. By your wording, I assume that order was not a factor in the problem, but if it was, we would double the 15 pairings we have in the solution to get 30 potential ordered pairings (since each ordered pair can be expressed in two ways, i.e. {a, b} and {b, a}). I hope that this proves useful to someone.
@@Trevtutor hey Trev. Your videos on Discrete mathematics really helped me improve my programming skills. Thank you so much. I just wanted to ask if you have any plans to make a series on statistics. Machine learning is a trending topic right now and statistics is at the core of it. I am sure a lot of people will find it helpful.
Excuse me; HUMAN meat?? Would you be willing to share your supplier? People get all defensive when they hear I'm in the market for human meat. Something about "morals" or "the law" or smth, idk
![[Discrete Mathematics] Rule of Sum and Rule of Product Examples](http://i.ytimg.com/vi/t0us-MXrFZg/mqdefault.jpg)
![[Discrete Mathematics] Rule of Sum and Rule of Product Examples](/img/tr.png)
Human meat, I could understand, but top bread =/= bottom bread is just crazy talk.
i couldnt agree more
i'll eat a baby but fuck if u think i'm gunna mix white and rye bread
I know right
Its "!=="
😂😂😂
I believe at 1:37 the Addition Rule should be A or B can be done in m+n ways.
My professors' notes didn't make sense, I couldn't figure out the homework.. you just helped me LOADS! now i don't feel like crying in the library lol
is no one actually talking about the human meat part????
There are hardly any comments here. Of course no one is talking about it. Yet.
Best thing is that its when we have different kinds of bread we go wild not on the human meat part :D
bro, that is what I am thinking right now, what? human meant?
i was just about to
@Lau taro no
So for some reason this was the most complicated topic ever when my actual prof described it. thanks!
Great video! It's helped me out a ton. Thanks! Made it so much simpler than my tutor.
Hey i remeber this channel, glad to see u still make content :)
I am prepping for my exam with your videos. I love your content, they're easily digestible.
me too unfortunately
lol that was a good laugh "human meat" thanks for the vid. So much better then my animation zybooks.
Hey Trev... We were introduced to you by our lecturer Dr Morton is S.A. You are so good in explaining.. Do you mind in helping me here; " Qn: How many different 4-digit natural numbers containing only odd digits are there? "
I think it is 5×5×5×5=625
Thanks man. I have an online textbook, with these absurd animations to teach myself. I hate Zybooks.
Love your teaching style
Bro you cracked me up when you mentioned the vowels 😂😂😂 eiaeiou 🙆??????? 7:10'
wow thank you this was awesome
While the licensee plate question is a perfect example part b is worded poorly. I interpreted the problem much differently combining 2 numbers, 1 odd number, 1 even number assuming we had to fit the criteria of a 6 character license plate. In other words, if you have 1 odd number and 1 even number then you already have at least 2 numbers and the same for 2 letters. If you contain at least 2 vowels then you already contain 2 letters.
Because of this, my final solution was: 5 * 5 * 5 * 5 * 36 * 36 = 5^4 * 36^2.
you have 5 choices of even and odd numbers, 5 choices for a vowel and then you can pick from 10 (numbers) + 26 (letters) 2x (36 * 36).
They should honestly teach the principles of set theory and discrete mathematics right after algebra before calc
Thank you, your video explained a lot
Yeah yeah human meat, is no one gonna talk about vegetable being in quotations?
😳
😳
😳
tomato is a fruit :)
@@rocas4087 Technically most vegetables are fruits according to the biological definition. Any vegetable with seeds is a fruit.
how can i thank you i have no words 😓❤❤
Amazing video!!
"We go wild here, top and bottom bread can be different."
Yes and the human meat... ?
god bless your channel
it's interesting how you manage to say "human meat" with a straight face at 3:25
thanks ma i appreciate
Did anyone notice that he was slightly snickering after reading 'Human' and said "leittuce"?
Is there a shorter way to write (c) at 9:10 ?
Never-mind, I watched the factorial video.
at around 5:50 with the license plate problem, does the order not matter? Wouldn't it be (5^3)*(26^3)*(# of ways you can mix numbers and letters)?
Edit: To be more explicit, on a license plate, wouldn't abc123 be difference from 1a2b3c?
In this example he said were not being specific on where they go. But it would be multiplied by 6 to handle the ordering of the strings.
@@Al-nj6ww Why by 6? At first, I thought it should be multiplied by 20 since there are 20 possible permutations for aaabbb (6!/(3!*3!))
But when we have a plate it can be 44bbb4 (20 possible ways to rearrange it to receive a different plate) but it also can be 12abc3 which would mean there are 6!=720 ways to rearrange the symbols and receive a completely different plate.
So with each specific plate, we have from 20 to 720 ways to rearrange it. I can't think of a way to have a general calculation considering the order.
Either that or the answer given in the video already takes the order into account, since in the last example with plates (c) we apply the rule of product which gives us the same answer as the application of the permutation formula ( P(n,r) = n! ÷ (n-r)! ) would give, meaning that order matters and that abcdef and fedcba are considered to be different plates.
Also the application of the permutation formula in the first example would give us 3*4*5*24*25*26 as an answer and the difference between this and 5^3*26^2 is that the second one allows the letters/numbers to repeat.
Overall, I think it's a bad example for this topic haha
just noticed your comment is 5 years old. well maybe someone else will join the discussion
Sorry, I'm a little confused on the license plate example part b.
If we only have six spaces, and one space needs to be an odd (5 options), one space needs to be an even (5 options), another 2 spaces needs to vowels (5x5 options) then we have two spaces remaining, where we could place one letter and one number (10x26) or two numbers (10x10) or two letters(26x26), but I don't understand how we have room for 10x10x26x26 options when only two spaces remain?
I was thinking it would be 5^4(26x26) or 5^4(10x26) or 5^4(10x10) depending on how we handled the last two spaces we have remaining after we satisfied odd/even and vowel criteria.
Can someone please show me where my intuition is off?
There are 8 things in (b) that we need, not 6.
TheTrevTutor thank you, I must have missed the part where you stated this would be an 8 space license plate the first time I watched it. I just went back and rewatched it and now I caught the part where you state that. Sorry my bad
Human is much more readily available than say....turkey in this mixed up world that we live in. ;)
why are u using 5 for the number of even numbers ...isn't zero considered neither even nor odd?
can you explain this please: i have an exam on tuesday so i need help asap
there are 6 boys
a boy and a buy are chosen how many choices?
I know this is five months late, but I am going to solve this for anyone who [may] scroll through these comments:
If you pick one boy from the possible six, then there will be five possible boys that could pair with him.
Moving on to the second boy, there will be four possible pairings with him. (Since the first boy has already been considered).
We repeat this process up through boy five, where we get three, two, and one pairing(s) respectively.
Note: No pairings are allocated for boy six since all of his pairs have already been listed.
Summing the values we have obtained, we get 5+4+3+2+1 = 15 possible pairings of two boys from a group of six.
By your wording, I assume that order was not a factor in the problem, but if it was, we would double the 15 pairings we have in the solution to get 30 potential ordered pairings (since each ordered pair can be expressed in two ways, i.e. {a, b} and {b, a}).
I hope that this proves useful to someone.
Yeee Jimmy
human sandwich perfect 👌
Why did you write in 6:47 10 firstly while you said you are taking 8 symboled license plate??
Because he was talking about the numbers to choose from from 1-9
Y is also a vowel
Sometimes
Human as a choice of meat haha 😂😂😂 Great video though
I've never seen that option at Subway
But you have already covered this topic in an earlier video. Is this a re-upload?
Some videos are being re-done for better quality and clarity.
@@Trevtutor hey Trev. Your videos on Discrete mathematics really helped me improve my programming skills. Thank you so much. I just wanted to ask if you have any plans to make a series on statistics. Machine learning is a trending topic right now and statistics is at the core of it. I am sure a lot of people will find it helpful.
Statistics-related series are on the mind but definitely not in the next few months.
Letter (c) could be expressed as 26!/20! I think it would be more elegant this way.
teacher: you are overthinking too much. -1 point
Only do that if you know that and your teacher doesn't get angry.
03:26 human meat??
How is human meat used for sandwich
14
lets say we have a sentence, how can we know that its an additions or a multiplication rule ?
Eating two different types of bread is "wild", but eating human as meat is normal. Ok.
I do not understand :'(
#notallamericans
My man forgot sometimes 'y' :(
bro that human meat threw me tf off 💀
zero is niether even nor odd
canibal
Dude laughed because he miss spelled lettuce and he has no problems with human meat
2mins before exam to come here
The sound quality is way to lowwwwww
Why is no one talking about human meat???
Excuse me; HUMAN meat??
Would you be willing to share your supplier? People get all defensive when they hear I'm in the market for human meat. Something about "morals" or "the law" or smth, idk
your human meat as meat for sandwich is giving me creeps dude lol
Why the fuck there is human meat in your choices for your sandwich?
4:20
Human meat¡¡¡???😏😏😏😏
WTF are you saying "human meat", have you lost you mind.