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AP EAMCET · Maths · Permutation Combination

5 men and 4 women are seated in a row. If the number of arragements in which one particular man and one particular woman are together is ' \(\alpha\) ' and the number of arrangements in which those two are not together is \(\beta\), then \(\alpha: \beta=\)

  1. A \(2: 7\)
  2. B \(2: 9\)
  3. C \(4: 5\)
  4. D \(7: 2\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(2: 7\)

Step-by-step Solution

Detailed explanation

\(\alpha = (9-2+1)! \times 2! = 8! \times 2\) \(\text{Total arrangements} = 9!\) \(\beta = 9! - \alpha = 9! - (8! \times 2)\) \(\beta = 9 \times 8! - 2 \times 8! = 8!(9 - 2) = 8! \times 7\) \(\alpha : \beta = (8! \times 2) : (8! \times 7) = 2 : 7\)