Question

Find the number of terms in the complete expansion of (x+y)^150 after like terms are collected together.

Answer 1

After complete expansion of $(x+y)^{150}$ we will get terms:

$k_{0}x^{150}, k_{1}x^{149}y^1, k_{2}x^{148}y^2,..., k_{n}x^{150-n}y^{n},..., k_{149}x^{1}y^{149},k_{150}y^{150}$

Total count of terms will be 151.

Due to formula of binomial theorem

$k_{n}=\binom{150}{n}=\frac{150!}{n!(150-n)!}$

$n=0, 1, 2, ..., 150$