Find the number of words formed by permuting all the letters of the following word: INTERMEDIATE

Explanation

There are `12`letters in the word 'INTERMEDIATE' out of which `2` are I'S, `2` are T'S, `3` are E'S and the rest are all distinct.

So, the total number of words
= `(12!)/(2!2!3!)`

=`(12×11×10×9×8×7×6×5×4×3×2!)/(2!2!3!)`

= `(12×11×10×9×8×7×6×5×4×3)/(2×3×2)`

= `11×10×9×8×7×6×5×4×3
= 19958400`