SOLUTION: If yu have 5 copies of one book 4 copies of each two books 6 copies each of three books and single copy of 8 book yu arrange it in______

SOLUTION: If yu have 5 copies of one book 4 copies of each two books 6 copies each of three books and single copy of 8 book yu arrange it in_______no. Of ways

Question 1094038: If yu have 5 copies of one book 4 copies of each two books 6 copies each of three books and single copy of 8 book yu arrange it in_______no. Of ways
Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

I will assume you mean arrange them on a shelf, in a single row....

It's a general principle; let's look at a simple example: 3 copies of one book ("A"), 2 of another ("B"), and 1 of a third ("C").

If all 6 books were different, the number of ways of arranging them would be 6!:

Imagine a list of all those 6! ways of arranging the 6 books. The 3 A books can be ordered in 3! different ways. That means every entry in the list occurs 3! times; so the list is too large by a factor of 3!. So the number of arrangements is now

Likewise, the 2 B books can be arranged in 2! different ways, so again the list is too large by a factor of 2!; the number of distinct arrangements is now

And since there are no more books with multiple copies, that is the final number of distinct arrangements.

In your problem, there are a total of 23 books, with 6 of one, 5 of another, and 4 of a third, with the rest being single books. Thus the number shown at the beginning of my response.

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