Question

how many different ways can 36 identical chairs be placed in rows if all rows have the same number of chairs, each chair is in exactly one row, and no row has more than 20 chairs or less than 3 chairs?

Answer 1

Answer and Explanation:

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.