There are 120 different ways of arranging the letters, U, K, M, I and C. All of these arrangements are listed in dictionary order, starting with CIKMU. Which position in the list does UKIMC occupy?
+128408 There are 24 ways to form "words" when C appears first
And 24 ways to form words whenever i appears first
And 24 ways to form words when K comes first
And 24 ways to form words when M appears first
So when U appears first, it will be in the 4 * 24 + 1 = 97th position
So we wiill have
UCIKM UICKM UKCIM
UCIMK UICMK UKCMI
UCKIM UIKCM UKICM
UCKMI UIKMC UKIMC
UCMIK UIMCK
UCMKI UIMKC
So....it occupies the 112th position
