The coefficient of $\;x^{1012}\;$ in the expansion of $\;(1+x^{n}+x^{253})^{10}\;$,(where $\;n \leq 22\;$ is any positive integer),is :

Question

$(a)\;1\qquad(b)\;10_{C_{4}}\qquad(c)\;4n\qquad(d)\;253_{C_{4}}$