Too big expansion !

Algebra Level 5

What is the coefficient of $x^{ 11 }$ in the expansion of $(1+x^{ 2 })^{ 4 }(1+x^{ 3 })^{ 7 }(1+x^{ 4 })^{ 12 }$ .

1 solution

Rohit Sachdeva
Aug 29, 2014

(x²)¹(x³)³

+(x²)²(x³)¹(x⁴)¹

+(x²)⁴(x³)¹

+(x³)¹(x⁴)²

Using the fact that coefficient of xⁿ in [(1+x)^m] is mCn

=(4C1x7C3) + (4C2x7C1x12C1) + (4C4x7C1) + (7C1x12C2)

= 140+504+7+462=1113