How to find number of words made using letters of word 'EQUATION' if order of vowels do not change Find number of words made using letters of word 'EQUATION' if order of vowels do not change.
My attempt:-  since we do not have to change the order of the vowels  hence, 
             _E_U_A_I_O_
we have $6$ places to fill the remaining letters. Therefore total number of cases $= C(6,3) \times 3! + 6 \times 3!= 156$ 
But the answer is $336$.

You need to put Q, T and N into a blank eight-letter word, and fill in the remaining five places with the vowels in the prescribed order. There are $3!=6$ ways to order the consonants, and $\binom{6}{3}=56$ choices of three positions to put them in. So the answer is $6\times56=336$.
