In how many ways can 3 novels, 2 mathematics books, and 1 chemistry book be arranged on a bookshelf if

# In how many ways can 3 novels, 2 mathematics books, and 1 chemistry book be arranged on a bookshelf if

J
240 points

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?

In how
jeffp

8.7k points

part (a)

If the books can be arranged in any order and there are 6 total books,

$$6!=720$$ arrangements

part (b)

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,

$$2! \cdot 3! \cdot 3!=72$$

different orderings

part (c)

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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