Question

How many different words ending and beginning with a consonant can be made out of the letter of the word EQUATION?

Answer 1

8 letters i.e. 3 consonants 5 vowels.

The consonants are to occupy $1^{st}$ and last place and it can be done in ${}^3{P}_2$ ways. We will now be left with 5 vowels and 1 consonant i.e. 6 letters which can be arranged in $6!$ ways. Hence the number of words under given condition is

${}^3{P}_2\times 6!=6\times 720=4320$.