SMO 2014 Senior Round 1 Question 30

Let $X=\{1,2,3,4,5,6,7,8,9,10\}$ and $A=\{1,2,3,4\}$. Find the number of 4-element subsets $Y$ of $X$ such that $10\in Y$ and the intersection of $Y$ and $A$ is not empty.