The number of ways in which 9 persons can be | vedclass

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Question

(D) To divide $9$ persons into three equal groups,we first select $3$ persons out of $9$,then $3$ out of the remaining $6$,and finally $3$ out of the

Vedclass · Accepted Answer

$280$

Vedclass · Answer

(D) To divide $9$ persons into three equal groups,we first select $3$ persons out of $9$,then $3$ out of the remaining $6$,and finally $3$ out of the remaining $3$.The number of ways to distribute $n$ items into $k$ groups of size $m$ (where $n = km$) is given by the formula $\frac{n!}{(m!)^k \cdot k!}$.Here,$n = 9$,$m = 3$,and $k = 3$.Total ways $= \frac{9!}{(3!)^3 \cdot 3!} = \frac{362880}{(6)^3 \cdot 6} = \frac{362880}{216 \cdot 6} = \frac{362880}{1296} = 280$.Therefore,the correct option is $D$.

The number of ways in which $9$ persons can be divided into three equal groups is

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