Eight books are placed on a shelf. three of them form a 3-volume series, two form a 2-volume series, and 3 stand on their own. in how many ways can the eight books be arranged so that the books in the 3-volume series are placed together according to their correct order, and so are the books in the 2-volume series?

480 ways

Explanation:

Given

There are 3-Volume series i.e.

No of ways in which they can be arranged in order is 2 i.e. or

For 2 volume series

There are two ways in which 2 volume series is arranged

Considering 3 volume books to be a single book denoted by a

and 2 volume books to be a single denoted by b

Thus we have to arrange a,b and 3 others books

No of ways in which 5 books can be arranged is 5!

also a and b can be arranged in two ways internally so

there are total of ==480 ways

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another line in the declaration of independence is that people have certain rights just because they are human. humans are capable of obeying the three natural rights john locke mentioned making them governable by these laws and therefore entitled to these rights as well.

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