The number of ways in which $12$ books can be put in three shelves with four on each shelf is

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

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

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

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None of these

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Solution

The correct option is A $\frac{12!}{(4!)^{3}}$
The number of ways in which $m n$ different items are divided equally into $M$ groups each of $N$ object is $\frac{m n!}{(n!)^{m}}$
$\Rightarrow$ In our case $m = 3; n = 4$
Or $\frac{12!}{(4!)^{3}}$
Hence, the answer is $\frac{12!}{(4!)^{3}} .$

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The number of ways in which 12 books can be put in three shelves with four on each shelf is

The correct option is A 12!(4!)3The number of ways in which mn different items are divided equally into M groups each of N object is mn!(n!)m⇒ In our case m=3;n=4Or 12!(4!)3Hence, the answer is 12!(4!)3.

The number of ways in which $12$ books can be put in three shelves with four on each shelf is

The correct option is A $\frac{12!}{(4!)^{3}}$
The number of ways in which $m n$ different items are divided equally into $M$ groups each of $N$ object is $\frac{m n!}{(n!)^{m}}$
$\Rightarrow$ In our case $m = 3; n = 4$
Or $\frac{12!}{(4!)^{3}}$
Hence, the answer is $\frac{12!}{(4!)^{3}} .$