Statement-1: If n is a natural number thenn2!(n!)n+1 is a natural number.Statement-2: The number of ways of dividing mn studentsinto m groups each containing n students is (mn)!m!(n!)m

# Statement-1: If n is a natural number then$\frac{\left({n}^{2}\right)!}{\left(n!{\right)}^{n+1}}$ is a natural number.Statement-2: The number of ways of dividing mn studentsinto m groups each containing n students is $\frac{\left(mn\right)!}{m!\left(n!{\right)}^{m}}$

1. A

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

2. B

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for
STATEMENT-1

3. C

STATEMENT-1 is True, STATEMENT-2 is False

4. D

STATEMENT-1 is False, STATEMENT-2 is True

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### Solution:

The number of ways of selecting students for
the first group is ; for the second group is  and

so on.

$\therefore$ the number of ways of dividing $\left(mn\right)$ students into m
numbered groups is

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