Soal :

Pada persamaan x1 + x2 + x3 + x4 = 12, xi adalah bilangan bulat >=0. Berapa jumlah kemungkinan solusinya?

Jawab :

Misalkan :

Analogi: 12 buah bola akan dimasukkan ke dalam 4 buah

kotak (dalam hal ini, n = 4 dan r = 12).

kotak (dalam hal ini, n = 4 dan r = 12).

Bagilah keduabelas bola itu ke dalam tiap kotak. Misalnya,

Kotak 1 diisi 3 buah bola (x1 = 3)

Kotak 2 diisi 5 buah bola (x2 = 5)

Kotak 3 diisi 2 buah bola (x3 = 2)

Kotak 4 diisi 2 buah bola (x4 = 2)

x1 + x2 + x3 + x4 = 3 + 5 + 2 + 2 = 12

Kotak 1 diisi 3 buah bola (x1 = 3)

Kotak 2 diisi 5 buah bola (x2 = 5)

Kotak 3 diisi 2 buah bola (x3 = 2)

Kotak 4 diisi 2 buah bola (x4 = 2)

x1 + x2 + x3 + x4 = 3 + 5 + 2 + 2 = 12

//pakai kombinasi boleh berulang

Cara = C(n+ r – 1, r)=C(4 + 12 – 1, 12) = C(15, 12) = 15C12 = 455 buah solusi.

Advertisements

mau nanya dong gan lanjut dr soal diatas… brp jumlah kemungkinan solusi jika x1>1 ,x2>0 ,x3>3, x4>=0 ?

Wah, kalau itu sih ane masih belum menemukan jawabannya. Soal ini terlalu rumit menurut ane. Maaf ya telat balasnya 🙂

Saved as a favorite, I love your blog!

Very rapidly this website will be famous amid all blog visitors,

due to it’s nice content

Thanks 😀 Have a great week.

Thank you for your comment 🙂 and always stay tuned 😀

That is a really good tip esoecially to those new to the blogosphere.

Short but very accurate info… Appreciate your shharing this one.

A must read post!

I was excited to uncover this web site. I wanted

to thank you for ones time just for this wonderful read!!

I definitely enjoyed every part of it and I have you book marked to

look at new information in your blog.

I think the admin of thi ѕite is in fact working hard in suppоrt of his

web page, becaսse heгe every material is quality based material.

Hey There. I found your blog the usage of msn. That

is a really well written article. I’ll make sure to bookmark it and come back to read more of your helpful information. Thank you for the post.

I will certainly comeback.