If the different permutations of all the ...

NCERT Class XI Mathematics - Permutations and Combinations - Solutions

Question : 34 of 41

Marks: +1, -0

If the different permutations of all the letters of the word EXAMINATION are listed as in a dictionary, how many words are there in this list before the first word starting with E ?

Solution:

Total no. of letters in the word EXAMINATION are 11 with 2 A’s, 2I’s and 2N’s.

Now when word starts with A i.e., A is fixed at the beginning of the word.

Then we have to arrange the remaining 10 letters with 2I’s, 2N’s.

Then no. of words starting with A =

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

= 907200

∴ Required no. of words = 907200.

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