Examveda
Examveda

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

Answer: Option B

Solution(By Examveda Team)

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

Join The Discussion

Related Questions on Permutation and Combination