anonymous
  • anonymous
In how many ways can you write 18 as the sum of three counting numbers?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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zzr0ck3r
  • zzr0ck3r
hmm what class is this for?
anonymous
  • anonymous
algebra 2/Trig
zzr0ck3r
  • zzr0ck3r
Is this a homework problem, or are you just curious? This is a question for combinatorics.

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anonymous
  • anonymous
this is review for the test tomorrow. I think my teacher is trying to start us on pre calc for next year so i think thats what this is.
zzr0ck3r
  • zzr0ck3r
Do you have any idea how you are supposed to solve this?
anonymous
  • anonymous
on these type of combination problems we've been using factorials, and sometimes exponential functions, but I don't know where to start on this one
zzr0ck3r
  • zzr0ck3r
3! = 6 6 + 6 + 6 10+7+1 10+5+3 10+6+2 .......
zzr0ck3r
  • zzr0ck3r
are counting numbers just natural?
anonymous
  • anonymous
so its 3 ! ?
zzr0ck3r
  • zzr0ck3r
I can list much more than three if I understand the question right. But I don't think I do
zzr0ck3r
  • zzr0ck3r
err much more than 6
anonymous
  • anonymous
we've also been using pascals triangle if that helps.
zzr0ck3r
  • zzr0ck3r
@Luis_Rivera can you explain please
anonymous
  • anonymous
is it possible that it has something to do with the 18th row? or 18!/(3!15!) or something?
zzr0ck3r
  • zzr0ck3r
I have no idea, maybe luis will answer.
anonymous
  • anonymous
haha I hope so
zzr0ck3r
  • zzr0ck3r
but I can list way more than 6 ways of writing 18 with the sum of three natural numbers
anonymous
  • anonymous
10 + 5 + 3= 5 *2 + 5 + 3 primez : 5, 3, and 2 6 + 4 + 8 = 3*2 + 2*2 + 2^3 And on and on, notice that even though you see a 5, the actual numbers used total 3. Anyway that's how I was taught in ancient India
zzr0ck3r
  • zzr0ck3r
ahh I see.
zzr0ck3r
  • zzr0ck3r
so its how many numbers are used, not 3 numbers added together.
zzr0ck3r
  • zzr0ck3r
bah im still confused...lol gl @liv2dance
tkhunny
  • tkhunny
We seem to be ignoring repeats. it does NOT say 3 DISTINCT values. Try expanding this \(\left(\sum\limits_{n = 1}^{16}x^{n}\right)^{3}\), and just reading the coefficient off the resulting \(x^{18}\) term. I get 136.
anonymous
  • anonymous
I know it does not say distinct values, but they must be assumed, like in permutations of a word. Even though they do not say distinct you will not use the same word twice
anonymous
  • anonymous
i think @tkhunny is right though.
anonymous
  • anonymous
I don't see what the prime numbers have to do with finding the amount of (__+__+__) that equals 18
tkhunny
  • tkhunny
Generating function can be tedious, to be sure, but the idea is not overwhelming.
anonymous
  • anonymous
Haha sorry. I'm almost positive @tkhunny is right. Thanks for everyones help though

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