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The letters of the word TOUGH are written in all possible orders and these words are written out as in a dictionary, then the rank of the word TOUGH is
  • a)
    120
  • b)
    88
  • c)
    89
  • d)
    90
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The letters of the word TOUGH are written in all possible orders and t...
Rank = (4!x 3) + (3!x 2) + (2!x 2)+ 1 = 72 + 12 + 4 + 1 = 89
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Most Upvoted Answer
The letters of the word TOUGH are written in all possible orders and t...
Rank of a word in dictionary order

In a dictionary, words are arranged in a certain order, known as the dictionary order. The rank of a word in this order is the position of the word in the list of all the words formed by rearranging the letters of the given word.

Example: The word 'CAT' can be rearranged in 6 ways: CAT, CTA, ACT, ATC, TAC, TCA. In the dictionary order, these words appear as follows:

ACT
CAT
TAC
ATC
CTA
TCA

The rank of the word CAT is 2, since it appears second in the list.

Solution:

The word TOUGH can be rearranged in 5! = 120 ways. These words can be arranged in the dictionary order as follows:

GOTUH
GOUTH
GOTHU
GOUHT
GOTHU
GOUTH
GTUOH
GTOUH
GTUHO
GTOHU
GTHOU
GTHUO
GUOTH
GUTOH
GUHOT
GUHTO
GUTHO
GUTHO
HOTUG
HOUGT
HOTGU
HOUTG
HOTUG
HOUGT
HTUOG
HTOUG
HTUGO
HTOGU
HTOGU
HTGOU
HUOGT
HUOTG
HUOGT
HUOTG
HUTGO
HUTOG
OGTUH
OGUTH
OGTHU
OGTUH
OGUTH
OGHTU
OGHUT
OGHTU
OGHUT
OGUHT
OGUTH
OTGUH
OTGHU
OTUGH
OTUHG
OTHGU
OTHUG
OUTGH
OUTHG
OUGHT
OUGHT
OUHTG
OUHGT
OUTGH
OUTHG
TGUOH
TGOUH
TGHUO
TGHOU
TGOHU
TGOUH
TUOGH
TUOHG
TUGHO
TUGOH
TOUGH
TOUGH
TOGUH
TOGHU
TOUGH
TOUHG
TOHGU
TOHUG
TOUTG
TOUGH
TUGHO
TUGOH
THUOG
THOUG
THGUO
THGOU
THOGU
THOUG
TUGHO
TUGOH
TUOGH
TUOHG
TUGHU
TUGOH
UGOTH
UGOTU
UGHOT
UGHTO
UGTOH
UGTHO
UOGHT
UOGTH
UOHGT
UOHTG
UOTGH
UOTHG
UTHGO
UTHOG
UTOGH
UTOHG
UTHOG
UTHGO
UGOTH
UGOTU
UGHOT
UGHTO
UGTOH
UGTHO
UOGHT
UOGTH
UOHGT
UOHTG
UOTGH
UOTHG
UTHGO
UTHOG
UTOGH
UTOHG
UTHOG
UTHGO

The word TOUGH appears as the 89th word in this list. Therefore, the rank of the word TOUGH is 89.

Therefore, option (c) 89 is
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The letters of the word TOUGH are written in all possible orders and these words are written out as in a dictionary, then the rank of the word TOUGH isa)120b)88c)89d)90Correct answer is option 'C'. Can you explain this answer?
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