Question 1044846: An exercise class has 28 participants. The instructor arranges the participants in rows. Each row has the same number of participants. How many possible arrangements are there?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! Possibility # 1: 1 row of 28
# 2: 2 rows of 14
# 3: 4 rows of 7
# 4: 7 rows of 4
# 5: 14 rows of 2
# 6: 28 rows of 1
If the participants are clones,
or if we do not care who is in each position,
I would say that makes 6 possible arrangements.
I would choose that interpretation.
If you interpret the plurals in "rows" and "participants" to mean there could not be just 1 row,
or just 1 participant in each row,
Then there are 4 arrangements of positions.
If we care who is in each position, then we have to multiply the number found before (6 or 4) times a very large factor.
That factor is 28! = 28×27×26×.....×3×2×1 = about 3.05×10^29.
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