Q57 / 160 · AP EAMCET 2022 (08 Jul Shift 2) · Mathematics

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

A
$(200) ! /(201)^{20} \cdot 10 !$
B
$(200) ! /(10 !)^{10} \cdot 20 !$
Correct answer
C
$(200) ! /(20 !)^{10} \cdot 10 !$
D
$(200) ! /(10 !)^{20} \cdot 20 !$

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 $=\frac{(200) !}{(20 !)^{10},(10 !)}$

Hence, the correct answer is option: 'C'.

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