(A) To divide $n$ distinct objects into $k$ groups of equal size $m$ (where $n = m \cdot k$),the number of ways is given by the formula: $\frac{n!}{(m

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(A) To divide $n$ distinct objects into $k$ groups of equal size $m$ (where $n = m \cdot k$),the number of ways is given by the formula: $\frac{n!}{(m!)^k \cdot k!}$.Here,$n = 15$,$m = 3$,and $k = 5$.Substituting these values into the formula,we get the number of ways as $\frac{15!}{(3!)^5 \cdot 5!}$.Therefore,the correct option is $A$.

Competitive Quantitative Aptitude Permutation and Combination Permutation and Combination

Medium

Choose the correct number of ways in which $15$ different books can be divided into five heaps of equal number of books.

A
$\frac{15!}{(3!)^5 \cdot 5!}$
B
$\frac{15!}{(3!)^5}$
C
$^{15}C_5$
D
$^{15}P_5$

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Choose the correct number of ways in which $15$ different books can be divided into five heaps of equal number of books.

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