Question

How many words can be formed with letters of word $DOGMATIC$ when $O,A,I$ are (i) always together (ii) never together.

Answer 1

DOGMATIC

Vowels OA1, Consonants, D,G,M,T,C

(I) always together

$6!\times 3!$

$\Rightarrow 720\times 6=4320$

$=4320$ ways

(II) Never together

$8!-(6!\times 3!)$

$=6!(8\times 7-3\times 2)$

$=6!(56-6)=50\times 720$

$=3600$ ways