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The five letters of the word CHAIR are arranged at random in a row. What is the probability that the two vowels A and I stand next to each other?

Competition practiceData & Probability
  • A1/5
  • B3/5
  • C2/5
  • D1/10

Step-by-Step Solution

The 5 different letters can be arranged in 5! = 120 ways. Tying A and I into a single block leaves 4 items, arranged in 4! = 24 ways, and the block itself can be ordered in 2! = 2 ways, giving 48 favourable arrangements. Probability = 48/120 = 2/5. (3/5 is the probability that the vowels are apart.)
Answer: C) 2/5

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