Find Rank of the word LUMINESCEN in the dictionary of words formed by the letters of the word LUMINE

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04 Apr 2019 Rank of the word

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

OPtion

1) 441221
2) 444221
3) 449221
4) 442221
5) 445221
6) 448221
7) 447221
8) 446221
9) 443221
10) None of these

Solution

Answer: 449221

luminescen
Lets arrange the letters alphabetically = ceeilmnnsu

Words starting with c = 9!/(2!*2!) = 90720
Words starting with e = 9!/(2!) = 181440
Words starting with i = 9!/(2!*2!) = 90720
Words starting with lc = 8!/(2!*2!) = 10080
Words starting with le = 8!/(2!) = 20160
Words starting with li = 8!/(2!*2!) = 10080
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 = 449221

Option 3)

Correct Option: 3 Best Solution (3)

AASHRAY AJAY SHARMA   5 years AGO

L--4/(2!×2!) x 9! = 362880
U--8/(2!×2!) x 8! = 80640
M--4/(2!×2!) x 7! = 5040
I--3/(2!×2!) x 6! = 540
N--3/(2!×2!) x 5! = 90
E--1/2! x 4! = 12
S--3/0! x 3! = 18
C--0/0! x 2! = 0
E--0/0! x 1! = 0
N--0/0! = 0

=>362880 + 80640 + 5040 + 540 + 90 + 12 + 18 + 0 + 0 + 0 =>449220
=>449220 + 1 = 449221
i.e., Rank of the word 'LUMINESCEN' = 449221 Option 3

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suryanarayana   5 years AGO

luminescen=>4853627126
and considering directionary numbers we can write 362880+80640+5040+540+90+12+18+1
449221

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G.S.Kantharao   5 years AGO

362880 + 80640 + 5040 + 540 + 90 + 12 + 18 + 0 + 0 + 0 = 449220
449220 + 1 = 449221
Hence right option is 3👈

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