Seven white balls and three black balls are randomly placed in a row. The probability that no two black balls are placed adjacently, equals :

Options

A. `(1)/(2)`
B. `(7)/(15)`
C. `(2)/(15)`
D. `(1)/(3)`

Answer

B

Explanation

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)`