There are three copies each of 4 different books. In how ways can they be arranged in a shelf?

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Solution

There are three copies each of 4 different books.

$∴$ Total number of copies = 12

$∴$ Total number of ways in which these copies arranged in a shelf = $\frac{12!}{3! 3! 3! 3!}$

= $\frac{12!}{(3!)^{4}}$

Hence, required number of ways = $\frac{12!}{(3!)^{4}}$

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There are three copies each of 4 different books. In how ways can they be arranged in a shelf?

There are three copies each of 4 different books. ∴ Total number of copies = 12 ∴ Total number of ways in which these copies arranged in a shelf = 12!3!3!3!3! = 12!(3!)4 Hence, required number of ways = 12!(3!)4

There are three copies each of 4 different books.

$∴$ Total number of copies = 12

$∴$ Total number of ways in which these copies arranged in a shelf = $\frac{12!}{3! 3! 3! 3!}$

= $\frac{12!}{(3!)^{4}}$

Hence, required number of ways = $\frac{12!}{(3!)^{4}}$