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Three boxes are labeled as A ,   B and C and each box contains 5 balls numbered 1 ,   2 ,   3,   4 and 5 . The balls in each box are well mixed and one ball is chosen at random from each of the 3 boxes. If α ,   β and γ are the number on the ball from the boxes A ,   B and C respectively, then the probability that α = β + γ is equal to

Options

  1. A1 25
  2. B2 25
  3. C4 25
  4. D1 5

Correct answer

B. 2 25

Step-by-step solution

The total cases = 5 3 ∵ α = β + γ The possible cases are 2 , 1,1 , 3 , 1 , 2 , 3 , 2 , 1 , 4,1 , 3 4,3 , 1 , 4,2 , 2 , 5,3 , 2 5,2 , 3 , 5,4 , 1 5,1 , 4 So, the number of favourable cases = 10 Hence, the required probability = 10 5 3 = 2 25

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