Rank of the word EUCALYPTUSin the dictionary of words formed by the letters of the word EUCALYPTUS

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25 Jan 2017 Rank of word

Rank of the word EUCALYPTUSin the dictionary of words formed by the letters of the word EUCALYPTUS

OPtion

1) 488979
2) 488980
3) 488939
4) 488940
5) 488959
6) 488960
7) 488920
8) 488919
9) 488999
10)488990

Solution

Arranging letters in alphabetical order: ACELPSTUUY, only U is repeated (2 U’s)
Words starting with Alphabet A = 9!/2!
Words starting with Alphabet C = 9!/2!
Words starting with Alphabet EA = 8!/2!
Words starting with Alphabet EC = 8!/2!
Words starting with Alphabet EL = 8!/2!
Words starting with Alphabet EP = 8!/2!
Words starting with Alphabet ES = 8!/2!
Words starting with Alphabet ET = 8!/2!
Words starting with Alphabet EUA = 7!
Words starting with EUCALP= 4!
Words starting with EUCALS= 4!
Words starting with EUCALT= 4!
Words starting with EUCALU= 4!
Words starting with EUCALYPS = 2!
Words starting with Alphabet EUCALYPTS= 1
And next word is EUCALYPTUS
Sum of all words = 2*9!/2! + 6*8!/2! + 7! + 4*4! + 2! +1 = 488980

Option 2)

Correct Option: 2 Best Solution (2)

Ajay Sharma   7 years AGO

EUCALYPTUS
Now according to rank,
2*9!+3*8!+1+0*6!+0*5!+4*4!+0*3!+1*2!+1*1!+0*0!+1=488980

Like? Yes (1) | No   

Mukund Manohar   7 years AGO

Total no. of words = 10*9*8*7*6*5*4*3*2*1/2*1 = 1814400
Rank of word EUCALYPTUS
= (1814400/10)*2 + (181440/9)*6 + (40320/8)*1 + (5040/7)*0 + (720/6)*0 + (120/5)*4 + (24/4)*0 + (6/3)*1 + (2/2)*1 + 1
= 362880 + 120960 + 5040 + 0 + 0 + 96 + 0 + 2 + 1 + 1
= 488980

Like? Yes (1) | No