M4maths Previous Puzzles

06 Sep 2018 Rank of the word

Find Rank of the word MILLENNIUM in the dictionary of words formed by the letters of the word MILLENNIUM

OPtion

1) 121711
2) 121712
3) 121713
4) 121714
5) 121715
6) 121716
7) 121718
8) 121717
9) 121719
10) None of these

Solution

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

Sum of all = 121718

Option 7)

Correct Option: 7 Best Solution (0)