CA Foundation · Quantitative Aptitude · Permutations and Combinations
Seven distinct books are to be arranged on a shelf, including 2 particular books A and B. In how many arrangements are A and B NOT next to each other?
The answer is 3600. All 7 books can be arranged in 7! = 5040 ways. Treating A and B as one block gives 6! × 2! = 1440 arrangements with them adjacent. Subtracting, 5040 − 1440 = 3600 arrangements keep them apart.
- A1440
- B3600Correct
- C720
- D5040
Explanation
Total arrangements = 7! = 5040. Arrangements with A and B together = 6!×2! = 1440. Not together = 5040 − 1440 = 3600. The value 1440 is the 'together' count, a common slip.
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