Rank of a word in dictionary:-
If ‘ABC’ is arranged in dictionary order. find the rank of the word ‘CAB’
ABC → 1ˢᵗ
ACB →2ⁿᵈ
BAC → 3ʳᵈ
BCA → 4ᵗʰ
CAB → 5ᵗʰ → Answer
CBA → 6ᵗʰ
(Q). Find the rank of the word MOTHER when its letters are arranged in dictionary order.
Solution:-
Method (1) word ⇒ MOTHER
First arrange all the alphabets of the word in alphabetic order
now
(i) Total words starting with E = 5!
(ii) Total words starting with H = 5!
(iii) Total words starting with ME = 4!
(iv) Total words starting with MH = 4!
(v) Total words starting with MOE = 3!
(vi) Total words starting with MOH = 3!
(vii) Total words starting with MOR = 3!
(viii) Total words starting with MOTE = 2!
(ix) Total words starting with MOTHER = 1 ⇨ Final word
∴ Rank = 5! + 5! + 4! + 4! + 3! + 3! + 3! + 2! + 1
= 309 Answer
Method(2)
Add 1 in this value to find the rank of the final word = 308 + 1 = 309 Answer
(i) Assign numerical value according to order of alphabets
(ii) 2 numbers are less than 3 at its right side → (2, 1) ⇒ write 2 below M
(iii) 2 numbers are less than 4 at its right side → (2, 1) ⇒ write 2 below O
(iv) 3 numbers are less than 6 at its right side → (2, 1, 5) ⇒ write 3 below T
(v) 1 number is less than 2 at its right side → (1) ⇒ write 1 below H
(vi) 0 numbers are less than 1 at its right side ⇒ write 0 below E
(vii) There is no number after last number 5 ⇒ write 0 below R
Next Step ⇒ Starting from right side write 0!, 1!, 2!, …….
now multiply & add all these values & add 1 in this value to find the rank of desired final word.
Let’s take another example:-
(Q). Find the rank of the word ‘MEDICAL’ when arranged in dictionary.
Method(1)
word ⇒ MEDICAL
alphabetic order ⇒ ACDEILM
(i) Total words starting with A = 6!
(ii) Total words starting with C = 6!
(iii) Total words starting with D = 6!
(iv) Total words starting with E = 6!
(v) Total words starting with I = 6!
(vi) Total words starting with L = 6!
(vii) Total words starting with MA = 5!
(viii) Total words starting with MC = 5!
(ix) Total words starting with MD = 5!
(x) Total words starting with MEA = 4!
(xi) Total words starting with MEC = 4!
(xii) Total words starting with MEDA = 3!
(xiii) Total words starting with MEDC = 3!
(xiv) Total words starting with MEDIA = 2!
(xv) Total words starting with MEDICAL = 1 → Final word
∴ Rank = 6×6! + 3×5! + 2×4! + 2×3! + 2! + 1
=4743 Answer
Method (2)
now add 1 to this value to find the rank of the final word
∴ Rank = 4742 + 1 = 4743 Answer
Let’s take an Example with repetition
(Q). Find the rank of the word REPETITION
Solution:-
Method (1)
Hence rank of the final word = 323959 + 1
= 323960 Answer
Method (2)
REPETITION
EEIINOPRTT → 2E 2I 2T
(i) Total number of words starting with E = = 90720
(ii) Total number of words starting with I = = 90720
(iii) Total number of words starting with N = = 45360
(iv) Total number of words starting with 0 = = 45360
(v) Total number of words starting with P = = 45360
(vi) Total number of words starting with REE = = 1260
(vii) Total number of words starting with REI = = 2520
(viii) Total number of words starting with REN = = 1260
(ix) Total number of words starting with REO = = 1260
(x) Total number of words starting with REPEI = = 60
(xi) Total number of words starting with REPEN = = 30
(xii) Total number of words starting with REPEO = = 30
(xiii) Total number of words starting with REPETII = 3! = 6
(xiv) Total number of words starting with REPETIN = 3! = 6
(xv) Total number of words starting with REPETIO = 3! = 6
(xvi) Total number of words starting with REPETITIN = 1! = 1
(xvii) Total number of words starting with REPETITION = 1 ⇒ Final word
Add all above values = 32960
Hence Rank = 32960 Answer