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If the different permutations of all the letter of the words E

Question

If the different permutations of all the letter of the words $EX A M I N A T I ON$ are listed as in a dictionary, how many words are there in this list before the first word starting with $E$ ?

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Theodore Discussed

If the different permutations of all the letter of the words

EX A M I N A T I ON

are listed as in a dictionary, how many words are there in this list before the first word starting with

E

14 mins ago

Discuss this question LIVE

14 mins ago

Text solutionVerified

Arranging the words in dictionary order gives us

AA E II NNMOTX

Hence consider the words starting with A

A - - - - - - - - - -

The remaining 10 places can be arranged in

\frac{10 !}{2 ! \cdot 2 ! \cdot 2 !}

( as there are

2 A, 2 I, 2 N

)

The next letter that comes is

E .

Hence the

4, 53, 60 1^{s t}

word will be starting with E.

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Question Text	If the different permutations of all the letter of the words $EX A M I N A T I ON$ are listed as in a dictionary, how many words are there in this list before the first word starting with $E$ ?
Answer Type	Text solution:1
Upvotes	150