MILLENNIUM
Lets arrange the letters alphabetically = E II LL MM NN U
Words starting with E = 9!/(2!*2!*2!*2!) = 22680
Words starting with I = 9!/(2!*2!*2!) = 45360
Words starting with L = 9!/(2!*2!*2!) = 45360
Words starting with ME = 8!/(2!*2!*2!) = 5040
Words starting with MIE = 7!/(2!*2!) = 1260
Words starting with MII = 7!/(2!*2!) = 1260
Words starting with MILE = 6!/(2!) = 360
Words starting with MILI = 6!/(2!) = 360
Words starting with MILLEI = 4!/(2!) = 12
Words starting with MILLEM = 4!/(2!) = 12
Words starting with MILLENI = 3! = 6
Words starting with MILLENM = 3! = 6
Words starting with MILLENNIM = 1
and the required word is the next one MILLENNIUM
Sum of all = 121718
Words starting with lm = 8!/(2!*2!) = 10080
Words starting with ln = 8!/(2!) = 20160
Words starting with ls = 8!/(2!*2!) = 10080
Words starting with luc = 7!/(2!*2!) = 1260
Words starting with lue = 7!/(2!) = 2520
Words starting with lui = 7!/(2!*2!) = 1260
Words starting with lumc = 6!/(2!*2!) = 180
Words starting with lume = 6!/(2!) = 360
Words starting with lumic = 5!/(2!*2!) = 30
Words starting with lumie = 5!/(2!) = 60
Words starting with luminc = 4!/(2!) = 12
Words starting with luminec = 3! = 6
Words starting with luminee = 3! = 6
Words starting with luminen = 3! = 6
Words starting with luminescen = 1