Question

Number of words with or without meaning that can be formed using alphabets $A,C,E,F,I,J,O,R,S$ such that vowels should occupy even positions and $E,F,O,R$ should come together are

Answer 1

Place the alphabets $E,F,O,R$ in a box
The variations of $E,F,O,R$ can be,
$E,F,O,RE,R,O,FO,R,E,FO,F,E,R$
Total $=4$

When the box starts from $1^{\text{st}}$ place then the total words will be
$=4\times 2!\times 3!=48$
Same thing is repeated till $6^{\text{th}}$ place
Hence the total number of words
$=6\times 48=288$