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    Question

    A box contains ‘x’ indigo, ‘x – 4’ violet and

    ‘x – 8’ blue balls. If two balls are drawn at random then probability of getting a violet ball and an indigo ball together is 1/3. If three balls are drawn from the box, then find the probability of getting three different coloured balls.
    A 1/5 Correct Answer Incorrect Answer
    B 4/5 Correct Answer Incorrect Answer
    C 5/6 Correct Answer Incorrect Answer
    D 1/6 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Total number of balls in the box = x – 4 + x – 8 + x = 3x – 12

    According to question;
    { (x – 4) C 1 ×  x C 1 }/ (3x – 12) C 2  = 1/3
    Or, 3 × {2 × (x – 4) × x} = (3x – 12) × (3x – 13)
    Or, {2 × (x – 4) × x} = (x – 4) × (3x – 13)
    Or, 2x 2  – 8x = 3x 2  – 25x + 52
    Or, x 2  – 17x + 52 = 0
    Or, x 2  – 13x – 4x + 52 = 0
    Or, x(x – 13) – 4(x – 13) = 0
    Or, (x – 4)(x – 13) = 0
    Or, x = 13 or x = 4 (not possible)
    Number of indigo balls = 13
    Number of violet balls = 13 – 4 = 9
    Number of blue balls = 13 – 8 = 5
    Total number of balls = 3 × 13 – 12 = 27
    Desired Probability = ( 13 C 1 ×  9 C 1  × 5 C 1 )/ 27 C 3  = (6 × 13 × 9 × 5)/(27 × 26 × 25) = 1/5

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