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

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(A) To divide $9$ persons into $3$ equal groups of $3$ persons each,we first select $3$ persons out of $9$,then $3$ out of the remaining $6$,and final

Vedclass · Accepted Answer

$280$

Vedclass · Answer

(A) To divide $9$ persons into $3$ equal groups of $3$ persons each,we first select $3$ persons out of $9$,then $3$ out of the remaining $6$,and finally $3$ out of the remaining $3$.Since the order of the groups does not matter,we divide by $3!$.The number of ways is given by $\frac{\binom{9}{3} \binom{6}{3} \binom{3}{3}}{3!} = \frac{\frac{9!}{3!6!} 	imes \frac{6!}{3!3!} 	imes \frac{3!}{3!0!}}{3!} = \frac{9!}{(3!)^3 	imes 3!}$.Calculating the value: $\frac{9 	imes 8 	imes 7 	imes 6 	imes 5 	imes 4}{6 	imes 6 	imes 6} = \frac{60480}{216} = 280$.

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

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