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1998

JEE Main 1998 Mathematics question on Probability

Seven white balls and three black balls are randomly placed in a row. The probability that no two black balls are placed adjacently, equals
  1. A.
    12\dfrac{1}{2}
  2. B.
    715\dfrac{7}{15}
  3. C.
    215\dfrac{2}{15}
  4. D.
    13\dfrac{1}{3}
Show answer and solution

Correct option: B

Solution

The 7 white balls create 8 gaps (including ends). Choose 3 of these 8 gaps for the black balls: C(8,3) = 56 ways. Total ways to place 3 black balls among 10 positions: C(10,3) = 120. Probability = 56/120 = 7/15.

[1998]

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