Homework Statement
# of integer solutions of x1+x2+x3+x4 = 32
where x1,x2,x3>0 and 0<x4≤25
Homework EquationsThe Attempt at a Solution
So in the case where x4 = 25 we have
x1+x2+x3= 4
in the case where x4 = 24 we have
x1+x2+x3 = 5
...
in the case where x4 = 1 we have
x1+x2+x3 = 28so...
Homework Statement
Coefficient of xy(z^-2) in (x-2y+3(z^-1))^4
Homework EquationsThe Attempt at a Solution
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I was wondering if anyone could give me an explanation for my answer?
The coeffecient of xy(z^-2) does not = 4 where I would be able to use the multinomial theorem.
So since I...
Yes the cans are identical.
My question is, say you have 3 identical cans, and 3 distinguishable people.
How many ways can I distribute these 3 cans to the 3 people. A person doesn't have to have any, or can have all of the cans.
So the possibilities are: Person A gets 0-3 cans, Person B get...
Homework Statement
Hi say I have 2 identical tin cans and I want to hand it out to three people B,C,D
I have three ways of doing this by giving all 2 cans to person B, then to person C, then to person D.
Then I have another 2 ways by giving person B 1 can, and C one can. Also person B 1 can...
That really does seem like a simple proof. Do you know what book I should read after basic mathematics? I want a solid foundation in math so that I can be kind of like a "jack of all trades" and learn topics from other fields like computer science, physics, engineering. I'm just now getting...
I've realized that a lot of textbook questions require me to google things because I have no clue how to prove certain things.
For example, I do not have the fact that if the last 2 digits in a number are divisible by 4, that number is then divisible by 4.
I'm pretty sure my teacher will not...
Thank you! I think I'm starting to understand now! There are k= 14 books.
Truly I thank you for the reply and I don't understand why I couldn't see this problem this way the first time... IDK what I was thinking in the OP
So there are 15! arrangements. Then there are 14 cases like I listed.
That's 15!*14 its starting to make sense now.. but I just don't see why my logic is faulty in the OP.
for example 1 book on shelf L, 14 on shelf R. You have 15 books that can be on shelf L, 14! combinations on shelf R =...
Homework Statement
Pamela has 15 different books. In how many ways can she place her books on two shelves so that there is at least one book on each shelf. (consider the books in each arrangement to be stacked one next to the other, with the first book on each shelf at the left of the shelf)...
So at what point can I just define something without proving its true and have a result that's true regardless if the definition is true or not
I guess what a better way to say is when can I make an assumption?
Wouldn't
"So if I define a^1 to be = (a)(1)
and a^n to be = (1)(a)(a)...(a) with the product being taken n times
and a^m to be = (1)(a)(a)...(a) with the product being taken m times
"
allow it to constituted as a proof though, since I'm defining it in that way?
I'm trying to prove that a^0 is = 1
So if I define a^1 to be = (a)(1)
and a^n to be = (1)(a)(a)...(a) with the product being taken n times
and a^m to be = (1)(a)(a)...(a) with the product being taken m times
a^n * a^m would then = (1)[(a)(a)...(a) with the product being taken n times * and...