Hi nsuen,

The "math" behind Permutation questions will be influenced by the restrictions that the prompt gives you to work with, so you have to pay careful attention to how these questions are worded.

Here, we know that there are 5 people and that they're sitting around a circular table. This is different from 5 chairs that are in a row (which would be a much easier calculation).

With 5 seats in a row, we'd have 5x4x3x2x1 = 120 arrangements....BUT since we have a circular table, some of these arrangements are duplicates. With 5 chairs, there are 5 "starting spots" that would lead to duplicates. For example...

ABCDE
BCDEA
CDEAB
DEABC
EABCD

These 5 options are actually the SAME option, since the letters are sill in order "going around" the table. We can't count this as 5 options; it's just 1 option.

So the math becomes: 5!/5 = 5x4x3x2x1/5 = 24

GMAT assassins aren't born, they're made,
Rich

Hi nsuen,

Since you have 5 people sitting at a circular table, you divide by 5 because rotating the people in either direction does NOT create a new arrangement.

Try drawing a circle, then write A, B, C, D and E on it (representing the 5 people). If you rotate the drawing, it might look like the people are in different spots, but the arrangement does NOT change. The 5 people sit in the same arrangement (even if it's oriented differently), but you're not allowed to count that arrangement 5 times - you only get to count it ONCE. Thus, you have to divide the total by 5.

GMAT assassins aren't born, they're made,
Rich