This is a circular permutation. " If n distinct things are to be arranged around a table, they can be arranged in (n-1)! ways"

Why did we take (n-1)?? In a circular arrangement, what is the starting point??? We dont know that. Hence we pick 1spot and count that as the starting point. Which means there are now 4places to be filled with 4knights and this can be done in 4! ways = 24

Its not just you. So, don't worry....

Let me first share with you a couple of formulae related to circular permutations. Digest them with logic & you will start getting a grip on these kind of problems.
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Number of circular permutations = n!/((n-r)!*L)
n --> number of objects in the source group
r --> number of objects selected
L --> number of possible locations for the first object placed.

So, based on information we have from the question, n=5 (source group), r=5 (selected) & L=5 (the number of locations for the first person to sit).

5!/((5-5)!*5) ==> 5!/5 ==> 4*3*2 ==> 24ways
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As Neo2000 mentioned, the number of ways the 5 kights can be seated at the round table is (n-1)!. This formula is derived from the above when n=r=L
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The above conditions are when there is a difference in clockwise & anti-clockwise arrangement.
When there is no difference in clockwise & anti-clockwise arrangement, the formula we should use is (n-1)!/2.

Hope this helps.