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AP EAMCET202318 May 2023Evening ShiftMathematicsProbabilityActual

A bag contains 12 two rupee coins, 7 one rupee coins and 4 fifty paise coins. If three coins are selected at random, then the probability that the sum of the values of the three coins is not an integral multiple of a rupee is

Options

  1. A^4 ( ¹² C ₂ ^7 C ₂+ ¹² C ₁ ^7 C ₁+ ^7 C ₂ )+3 ( ¹² C ₁+ ^7 C ₁ ) ²³ C ₃
  2. B4 ( ¹² C ₁ ^7 C ₁+ ¹² C ₂+ ^7 C ₂ )+ ^3 C ₃ ²³ C ₃
  3. C4 ( ¹² C ₂ ^7 C ₁+ ¹² C ₁ ^7 C ₂ )+3 ( ¹² C ₁ ^7 C ₂ ) ²³ C ₃
  4. D4 ( ¹² C ₃+ ^7 C ₃ )+3 ( ¹² C ₁+ ^7 C ₁ ) ²³ C ₃

Correct answer

B. 4 ( ¹² C ₁ ^7 C ₁+ ¹² C ₂+ ^7 C ₂ )+ ^3 C ₃ ²³ C ₃

Step-by-step solution

The following cases are possible: (i) 1 fifty paisa coin, 1 two rupee coin, 1 one rupee coin. (ii) 2 two rupee coin, 1 fifty paisa coin (iii) 2 one rupee coin, 1 fifty paisa coin (iv) 3 fifty paisa coin Then the required probability is aligned & P = ^4 C ₁ ¹² C ₁ ^7 C ₁ ⁺¹² C ₁ ^4 C ₁+ ^7 C ₂ ^4 C ₁+ ^4 C ₃ ²³ C ₃ & P = ^4 ( ¹² C ₁ ^7 C ₁ ⁺¹² C ₂ ⁺⁷ C ₂ )+ ^4 C ₃ ²³ C ₃ aligned

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