Now if we were to arrange them on a bench then we would use following formula

n! i.e; 1st position can be taken by any 1 of the 5 knights, 2nd position can be taken by only 1 of the 4 knights because 1 knight has already taken the 1st position, simillarly 3rd position can be taken by any 1 of the 3 knights .......

Thus the formula is = no of ways the 1st position can be filled *no of ways the 2nd position can be filled *no of ways the 3rd position can be filled * no of ways the 4th position can be filled *no of ways the 5th position can be filled = 5*4*3*2*1 = 120

But in circular permutation for

distinct objects one has to elliminate all the repeations i.e; we must count all the possibilities only once but we can take both clockwise and anticlockwise as seperate arrangements

Let X,Y,Z,P and Q be the knights

........x

q.............y

p............ z

Here , x y z p q is a possible arrangement (clockwise) and x q p z y is also a possible arrangement (anticlockwise)

But y z p q x or z p q x y or q p z y x etc.. are not distinct arrangements.

Simillarly for ,

......x

p........... z

q........... y

and others

Thus we have the formula

(n-1)!, which elliminates all repeatitions.

But for

not distinct objects you have only one possible combination i,e; either clockwise or anticlockwise e.g. pearls in a necklace.

Thus we have the formula

(n-1)!/2Hope this helps