permutation and combination

There are 8 letters in the word EQUATION.

Out of these 5 are vowels and 3 are consonants

The extreme left place has to be filled by a consonant , this can be done in 5  ways.

Thwe extreme right place has to be  filled by a consonant, this can be done in 3 ways.

The remaining 6 places can be filled by the remaining 6 letters( after selecting 2 letters for the exteme left and extremem right place respectively)in P(6,6)=6! ways.

So ,

 by the fundamental principal of counting the total number of ways as required in the question is

5*(6!)*3=15*(6!)

=15*720

=10800.

Pl send each question seperately.