The coefficient of λ n μ n in the expansion of ( 1 + λ ) n ( 1 + μ ) n ( λ + μ ) n is

Step-by-step solution

Coefficient of λ n μ n in ( 1 + λ ) n ( 1 + μ ) n ( λ + μ ) n ⇒ Coefficient of λ n μ n in C 0 n + C 1 n λ + C 2 n λ 2 + … + C n n λ n × C 0 n μ n + C 1 n μ n - 1 + … + C n n × C 0 n λ n + C 1 n λ n - 1 μ + … + C n n μ n Clearly, coefficient of λ n μ n is C 0 3 + C 1 3 + C 2 3 + … + C n 3 = ∑ r = 0 n C r n 3