The number of 4 letter words that can be formed using the letters of the word EXPLAIN which begin with an vowel when repetitions are allowed is

4 letter words using the letters of the word EXPLAIN begin with vowel when repetations are allowed.

consider 4 places.

First place is to be filled with 3 vowels A, E, I in 3 ways.

Remaining 3 places can be filled using the 7 letters {E, X, P, L, A, I, N} in $7^3$ ways.

No of permutations $=3\times 7^3$

                                    $=3\times 343=1029$