In how many different ways can the letters of the word "LEADING " be arranged…
2026
In how many different ways can the letters of the word "LEADING " be arranged in such a way that vowels always come together .
- A.
750
- B.
720
- C.
600
- D.
650
Attempted by 307 students.
Show answer & explanation
Correct answer: B
Answer: 720
Key idea: Treat the three vowels as one group so they always stay together.
Count letters: vowels = E, A, I (3); consonants = L, D, N, G (4).
Treat the three vowels as a single item along with the four consonants: total items = 4 + 1 = 5. These can be arranged in 5! = 120 ways.
Arrange the vowels internally: 3! = 6 ways.
Total arrangements = 5! × 3! = 120 × 6 = 720.
Therefore, the required number of arrangements in which the vowels always come together is 720.