10 books are placed at random in a shelf. The probability that a pair of books will always be together is_________?
Correct answer: C. 1/5
- A. 1/10
- B. 9/10
- C. 1/5
- D. 3/10
Explanation
Treat the specified pair as one block. The block and the other 8 books can be arranged in 9! ways, and the pair can be internally ordered in 2 ways, so the probability is 2 x 9!/10! = 2/10 = 1/5. The common wrong choice is 1/10, which forgets that the two books can appear in either order.
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