An academic department offers 8 lower level courses: \(\lbrace L_1, L_2,\ldots, L_8\rbrace\) and 10 higher level courses: \(\lbrace H_1, H_2,\ldots, H_{10}\rbrace\). A valid curriculum consists of 4 lower level courses. and 3 higher level courses.

1. How many different curricula are possible?
2. Suppose that \(\lbrace H_1, \ldots, H_5\rbrace\) have \(L_1\) as a prerequisite, and \(\lbrace H_6\ldots,H_{10}\rbrace\) have \(L2\) and \(L_3\) as prerequisites. i.e.. any curricula which involve, say, one of \(\lbrace H_1, \ldots, H_5\rbrace\) must also include \(L_1\). How many different curricula are there?