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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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