CMA Foundation · Fundamentals of Business Mathematics and Statistics · Permutation and Combinations
Seven different books, of which 3 are on costing and 4 are on law, are arranged on a shelf. In how many ways can they be arranged so that all 3 costing books stay together?
The arrangements number 720. Treating the three costing books as one block gives five items to arrange in 5! = 120 ways, and the books inside the block can be ordered in 3! = 6 ways, so 120×6 = 720.
- A720
- B1440Correct
- C5040
- D840
Explanation
Treat the 3 costing books as one block. Then there are 5 items (block plus 4 law books), arranged in 5! = 120 ways. Within the block the 3 books can be ordered in 3! = 6 ways. Total = 120×6 = 720... check: 5 items means block + 4 books = 5, so 120×6 = 720. Hence the answer is 720.
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