All the letters of the word 'AGAIN' be arranged and the words thus formed are known as 'Simple Words'. Further two new types of words are defined as follows:
(i) Smart word: all the letters of the word 'AGAIN' are being used, but vowels can be repeated as many times as we need.
(ii) Dull word: All the letters of the word 'AGAIN' are being used, but consonants can be repeated as many times as we need.
Q. Number of 7 letter dull words inw hich no two vowels are together, is

Options

A. 402
B. 420
C. 840
D. 42

Answer

B

Explanation

Now, 3 vowels A,I,A are to be placed in the five available places.
`{{:("XNXGXNXNX"),(" OR"),("XNXGXGXGX"),(" OR"),("XNXGXGXNX):}`
Hence, required number of ways
`=.^(5)C_(3)xx(3!)/(2!)xx{(4!)/(3!)+(4!)/(3!)+(4!)/(2!2!)}`
`=30(4+4+6)=420`