A university is conducting a research study that involves a survey of 8 different departments: Mathematics, Biology, Chemistry, Physics, Engineering, History, Literature, and Art. Each department has a distinct number of faculty members: Mathematics (5), Biology (3), Chemistry (4), Physics (6), Engineering (7), History (2), Literature (4), and Art (3). The university wants to form a committee of 4 faculty members, ensuring that at least one faculty member comes from each department represented on the committee. How many different ways can the committee be formed under this condition?