In how many different ways can the letters of the word CAPITAL be arranged so that the vowels always come together?
A
120
B
360
C
720
D
840
E
None of these
Correct Answer: 360
Keeping the vowels (AIA) together, we have CPTL (AIA).We treat (AIA) as 1 letter.
Thus, we have to arrange 5 letters.
These can be arranged in 5! = (5 × 4 × 3 × 2 × 1) ways = 120 ways
Now, (AIA) are 3 letters with 2A and 1I
These can be arranged among themselves in
$$\frac{{3!}}{{2!}} = \frac{{3 \times 2 \times 1}}{{2 \times 1}} = 3$$ ways
∴ Required number of ways = 120 × 3 = 360
