| Statement-1: \[\frac{({{n}^{2}})!}{{{(n!)}^{n}}}\] is a natural number for all\[n\in N\]. |
| Statement-2: The number of ways of distributing \[mn\] things in \[m\] groups each containing \[n\] things is\[\frac{(mn)!}{{{(n!)}^{m}}}\]. |
A) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
B) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
C) Statement-1 is true, Statement-2 is false.
D) Statement-1 is false, Statement-2 is true.
Correct Answer: A
Solution :
The number of ways of distributing \[mn\] things \[m\] groups each containing n things is\[\frac{(mn)!}{{{(n!)}^{m}}}\]here if \[m=n\], then \[\frac{({{n}^{2}})!}{{{(n!)}^{n}}}\] which must be a natural number.
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