Number of ways to get $xy^2$ from $(x+y+5)^5$ I am trying to understand a proof of counting number of trees using the conclusion of Cayley's formula.
At the end they got a $(x+y+5)^5$ and they say that the number of ways to get $xy^2$ from this is $5 \cdot \binom{4}{2} \cdot 5^2 = 750 $ and I can't figure how. Can someone please explain?
thanks.

$$(x+y+z)^n \to \dfrac{n!}{k_1!k_2!k_3!}x^{k_1}y^{k_2}z^{k_3} ,k_1+k_2+k_3=n\\$$
$$(x+y+5)^5 \to \dfrac{5!}{k_1!k_2!k_3!}x^{k_1}y^{k_2}5^{k_3} ,k_1+k_2+k_3=5\\ \to xy^2 \to ,1+2+k_3=5 \to k_3=2\\ \dfrac{5!}{1!2!2!}x^{1}y^{2}5^{2} \\25\dfrac{5!}{1!2!2!}x^{1}y^{2}=25\times 30 xy^2$$
