CA Foundation · Quantitative Aptitude · Permutations and Combinations
Seven different books are arranged on a shelf. In how many ways can this be done if two particular books must NOT be placed next to each other?
The answer is 3600. All seven books can be arranged in 5040 ways. Treating the two particular books as one block gives 6! × 2 = 1440 arrangements where they are adjacent. Subtracting gives 5040 − 1440 = 3600 ways.
- A1440
- B3600Correct
- C3840
- D5040
Explanation
Total arrangements = 7! = 5040. Arrangements with the two books together = 2 × 6! = 1440. Not together = 5040 − 1440 = 3600. Option 1440 is the 'together' count, the wrong case.
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