36 identical chairs must be arranged in rows with the same no of chairs in each row. Each row must contain at least 3 chairs and there must be at least 3 rows. A row is parallel to the front of the room. How many different arrangements are possible?

And, the number of rows = R

Since each row must have the same number of chairs. Therefore,

$C\times R=36.....\left(1\right)$

Since each row must contain at least 3 chairs and there must be at least 3 rows. Therefore, C and R both are greater than or equal to 3.

Thus, the possible arrangements are $3\times 12,4\times 9,6\times 6,9\times 4,12\times 3$.

Hence, there are 5 different arrangements are possible.

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