High School Pre-Cal

Question

What is the coefficient of the term containing m11n3 in the binomial expansion below?

(m+2n)^14



A.364

 

B.728

 

C.1,456

 

D.2,912

Answer 1

(m+2n)¹⁴ = ₁₄C₀m¹⁴(2n)⁰ + ₁₄C₁m¹³(2n)¹ + ₁₄C₂m¹²(2n)² + ₁₄C₃m¹¹(2n)³ + ...

 

Coefficient of the term containing m¹¹n³ is:

 

    ₁₄C₃(2³) = 8[14! / (3! 11!)]

 

                  = 8(14·13·12) / (3·2·1)

 

                  = 2,912