CA Foundation · Quantitative Aptitude · Seating Arrangements
In how many ways can 7 persons be seated around a circular table if three particular persons must always sit together?
The answer is 144. Treat the three persons as one block, giving 5 units around the table, which can be arranged in 4! = 24 ways. The block's members can be ordered in 3! = 6 ways. So the total is 24 × 6 = 144.
- A72
- B120
- C144Correct
- D720
Explanation
Treat the three persons as one block. The block and the other 4 persons make 5 units, which can be arranged around the table in (5-1)! = 24 ways. The three persons can be arranged within the block in 3! = 6 ways. Total = 24 × 6 = 144. Option 720 is wrong because it is 6!, which ignores the condition altogether.
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