In how many ways can 3 novels, 2 mathematics books, and 1 chemistry book be arranged on a bookshelf if
(a) the books can be arranged in any order?
(b) the mathematics books must be together and the novels must be together?
(c) the novels must be together, but the other books can be arranged in any order?
If the books can be arranged in any order and there are 6 total books,
The math books can be ordered in 2! ways, the novels can be ordered in 3! ways. The block of novels, math, and chemistry books can be ordered in 3! ways,
$$2! \cdot 3! \cdot 3!=72$$
The novels can be arranged in 3! ways and can occupy 4 different spaces, and the remaining books can be ordered in 3! ways,
$$4 \cdot 3! \cdot 3!=144$$
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