The number of different ways of dividing mn different things into n equal groups is

Question

The number of different ways of dividing mn different things into n equal groups is (A) ((m n) !/(m !)n ⋅ n !) (B) (( mn ) !/( n !) m ⋅ m !) (C) (( mn ) !/( m !) n ) (D) (( mn ) !/( n !) m )

Tardigrade Admin · Accepted Answer

Correct answer is (a) ((m n) !/(m !)n ⋅ n !)

Q. The number of different ways of dividing mn different things into $n$ equal groups is

$\frac{( mn )!}{( m ! ) ^{n} \cdot n !}$

$\frac{( mn )!}{( n ! ) ^{m} \cdot m !}$

$\frac{( mn )!}{( m ! ) ^{n}}$

$\frac{( mn )!}{( n ! ) ^{m}}$

Correct answer is (a) $\frac{( mn )!}{( m ! ) ^{n} \cdot n !}$

Q. The number of different ways of dividing mn different things into n equal groups is

(m!)n⋅n!(mn)!​

(n!)m⋅m!(mn)!​

(m!)n(mn)!​

(n!)m(mn)!​