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?

Guest Nov 21, 2019

#1**+1 **

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

CPhill Nov 21, 2019