Single correct option
In how many ways can the letters of the word GARDEN be arranged so that the two vowels always come together?
- A. 120
- B. 240
- C. 360
- D. 480
Show answer and solution
Answer: (B) 240
GARDEN has 6 distinct letters, with vowels A and E.
Treat the two vowels as a single block. This gives 5 units to arrange (the block plus the 4 consonants G, R, D, N): 5! = 120 ways.
Within the block, the two vowels can swap: 2! = 2 ways.
Total = 120 × 2 = 240.
Tip: 'Letters must stay together' → glue them into one unit, arrange all units, then multiply by the internal arrangements of the glued unit.
Treat the two vowels as a single block. This gives 5 units to arrange (the block plus the 4 consonants G, R, D, N): 5! = 120 ways.
Within the block, the two vowels can swap: 2! = 2 ways.
Total = 120 × 2 = 240.
Tip: 'Letters must stay together' → glue them into one unit, arrange all units, then multiply by the internal arrangements of the glued unit.
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