GMAT Club vs MGMAT on Combinatorics

[kathiepeng]

Hi, a GMAT club test question asks:

If 5 noble knights are to be seated at a round table, then how many different ways can they be seated?

a. 120
b. 96
c. 60
d. 35
e. 24 [they flag this as correct b/c they say it should be (n-1)!]

According to WT strat guide, a very similar example would infer the answer should be a. 120. The example is on pg 69: Arrangements of 4 people in 4 fixed chairs = 24.

Am I missing something here?

Thanks!

[jnelson0612]

Hi, a GMAT club test question asks:

If 5 noble knights are to be seated at a round table, then how many different ways can they be seated?

a. 120
b. 96
c. 60
d. 35
e. 24 [they flag this as correct b/c they say it should be (n-1)!]

According to WT strat guide, a very similar example would infer the answer should be a. 120. The example is on pg 69: Arrangements of 4 people in 4 fixed chairs = 24.

Am I missing something here?

Thanks!

That's a great question Kathie. The other problem must be assuming that the particular chair each knight sits in at the table is not relevant, which is different from placing people in five particular chairs.

For example, envision five chairs:
___ ___ ___ ___ ___

If I have ABCDE that is considered a different arrangement from EABCD.

However, now draw a round table and put five positions. Put ABCDE around in table in order. Now draw another circle and put EABCD around the table in order. Please notice that the knights are seated next to each other identically. The only difference is that they have rotated by one chair. This problem clearly doesn't care about WHICH particular chair the knights are in, only the arrangements of them next to each other, thus we can divide the 5! by the 5 chairs, since we don't care about that. I think this problem is a little deficient in not making it clear that the particular chair itself does not matter. Hope this helps!