#COMBINATORY

Question

Comments

same as chocolate problem

x1+x2+x3=10 unlimited repetation (n-1+rCr )

66 ans

---

no .

---

You did not apply bounds on values of x1,x2,x3 maybe one solution from 66 solution is (2,6,2) but we only have 5 blue balls?
I'm getting 18.

---

63 yes there is upper constraints using gf ..

Answer 1

X1+X2+X3=10

$0\leq X1\leq 10 , 0\leq X2\leq 5, 0\leq X3\leq 2$

[X^0+X^1+........X^10]^1 [X^0+X^1+........X^5]^1 [X^0+X^1+X^2]^1

(1-X^11)(1-X^6)(1-X^3) * 1/(1-X)^3

writing only required coeff.

(1-X^3-X^6+X^9) * 1/(1-X)^3

$\binom{3-1+10}{10} -\binom{3-1+7}{7}-\binom{3-1+4}{4}+\binom{3-1+1}{1}$

Solving above we get 18 ways