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?

Let the number of chairs = C
And, the number of rows = R
Since each row must have the same number of chairs. Therefore,
C×R=36               .....1
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 3×12, 4×9, 6×6, 9×4, 12×3.
Hence, there are 5 different arrangements are possible.
 

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