In the word EQUATION there are 5 vowels(A,E,I,O,U) and 3 consonants (Q,T,N)
There are 8 letters in EQUATION,
So to form different words that begin and end with consonants,
The first word can be filled with any of the three consonants – 3 ways
The last word can be filled with any of the remaining two consonants – 2 ways
The second word can be filled with any of the five vowels – 5 ways
The third word can be filled with any of the remaining four vowels – 4 ways
The fourth word can be filled with any of the remaining three vowels – 3 ways
The fifth word can be filled with any of the remaining two vowels – 2 ways
The sixth word can be filled with the remaining one vowels - 1 way
The seventh word can be filled with the remaining one consonant – 1 way
So Total no. of words = 3*2*5*4*3*2*1*1=720 words
