Class 11

Math

Algebra

Permutations and Combinations

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

$AAEIINNMOTX$

Hence consider the words starting with A

$A−−−−−−−−−−$

The remaining 10 places can be arranged in $2!⋅2!⋅2!10! $ ( as there are $2A,2I,2N$)

The next letter that comes is $E.$

Hence the $4,53,601_{st}$ word will be starting with E.