If 3n articles can be divided into 3 equal groups in 280 ways then n $=$

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Solution

The correct option is B $3$
$3 n$ articles can be divided into $3$ equal groups in $280$ ways
$\Rightarrow \frac{(3 n)!}{3! {(n!)}^{3}} = 280$
$\Rightarrow \frac{(3 n)!}{{(n!)}^{3}} = \frac{7.6.5.4.3.2.1}{3} = \frac{9.8.7.6.5.4.3.2.1}{216}$
$\Rightarrow n = 3$

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If 3n articles can be divided into 3 equal groups in 280 ways then n =

The correct option is B 33n articles can be divided into 3 equal groups in 280 ways⇒(3n)!3!(n!)3=280⇒(3n)!(n!)3=7.6.5.4.3.2.13=9.8.7.6.5.4.3.2.1216⇒n=3

If 3n articles can be divided into 3 equal groups in 280 ways then n $=$

The correct option is B $3$
$3 n$ articles can be divided into $3$ equal groups in $280$ ways
$\Rightarrow \frac{(3 n)!}{3! {(n!)}^{3}} = 280$
$\Rightarrow \frac{(3 n)!}{{(n!)}^{3}} = \frac{7.6.5.4.3.2.1}{3} = \frac{9.8.7.6.5.4.3.2.1}{216}$
$\Rightarrow n = 3$