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7 white balls and 3 black balls are kept randomly in order. Find the probability that no two adjacent balls are black.A. `(1)/(2)`B. `(7)/(15)`C. `(2)/(15)`D. `(1)/(3)`

Answer» Correct Answer - B
7 white and 3 black balls can be arranged in a row in `(10!)/(3!7!)` ways.
When 7 white balls are arranged in a row there are 8 place in between. In these 8 places 3 black balls can be arranged in `.^(8)C_(3)` ways.
`therefore` Required probability `=(.^(8)C_(3))/((10!)/(3!7!))=(7)/(15)`


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