We have 3 Physics books, 4 Math books, and 5 Chemistry books. The 12 books are distinct. We want to arrange them all on a bookshelf. Observe that without any restrictions there are 12! ways to arrange them on a bookshelf. Explain each answer. In how many ways can we do this (a) if the arrangement must start with a Physics book and must end with a Chemistry book? (b) if the arrangement cannot end with a chemistry book? (c) if the arrangement must begin with all the Physics books? (d) if the two specific books X and Y (of the 12 books) cannot be next to each other? (e) if all the books belonging to a subject must stay together (i.e. stay next to each other)? (hint: The subjects themselves have to be in some order.)
We have 3 Physics books, 4 Math books, and 5 Chemistry
books. The 12 books are distinct. We want to arrange them all on a
bookshelf. Observe that without any restrictions there are 12! ways to arrange
them on a bookshelf.
Explain each answer.
In how many ways can we do this
(a) if the arrangement must start with a Physics book and must end with a
Chemistry book?
(b) if the arrangement cannot end with a chemistry book?
(c) if the arrangement must begin with all the Physics books?
(d) if the two specific books X and Y (of the 12 books) cannot be next to
each other?
(e) if all the books belonging to a subject must stay together (i.e. stay next
to each other)? (hint: The subjects themselves have to be in some
order.)
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