Question

In how many different ways can the letters of the word TRAINER be arranged so that the vowels always come together?

• A. 1440
• B. 120
• C. 720
• D. 360

Answer 1

The correct option is D 360

(D) Treating (AIE). i.e., all the vowels together as one letter. Therefore, the word capital,
i.e., TRNR (AIE) can be arranged in $\frac{5!}{2}$ ways.(since R is repeated)
Since (AIE) can also be arranged in 3! ways, therefore, required number of ways
$=\frac{5!}{2}\times 3!=\frac{120\times 6}{2}=360$