How many words can be formed with the leters of the word 'EQUATION', which starts with a vowel and ends with a vowel?

Explanation

In the word 'EQUATION'
Vowels = E,U,A,I,O
Consonants = Q,T,N
If vowels are placed at 1st position and at last position, then no of ways to fill these two places with 5 vowels `= .^(5)P_(2)`
Now remaining places = 6 remaining letters = 3 vowels +3 consonants = 6
No. of ways to fill these 6 place with 6 letters `= .^(6)P_(6)`
From multiplication theorem,
Required permutations `=.^(5)P_(@) xx .^(6)P_(6)`
`=(lfloor5)/(lfloor3) xxlfloor6`
`= 4 xx5 xx 720`
`= 14400`