The number of ways of dividing 200 dissimilar things into 10 groups each containing 20 elements is

The number of ways of dividing 200 dissimilar things into 10 groups each containing 20 elements is
  1. $(200) ! /(201)^{20} \cdot 10 !$
  2. $(200) ! /(10 !)^{10} \cdot 20 !$
  3. $(200) ! /(20 !)^{10} \cdot 10 !$
  4. $(200) ! /(10 !)^{20} \cdot 20 !$

Solution

$\because$ Division of $m n$ objects into $m n$ groups of equal size is done by $\frac{(m n) !}{(n !)^m(m !)}$ Similarly, we have $m n=200 \Rightarrow n=20, m=10$ $\therefore$ Number of ways $=\frac{(200) !}{(20 !)^{10},(10 !)}$

Asked in: AP EAMCET 2022 (08 Jul Shift 2)

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