7 white balls and 3 black balls are kept randomly in order. Find the probability that no two adjacent balls are black.

Options

A. `(1)/(2)`
B. `(7)/(12)`
C. `(2)/(15)`
D. `(1)/(3)`

Answer

B

Explanation

The number of ways of placing 3 black balls without any restriction is `""^10 C_3` Since , we have total 10 places of putting 10 balls in a row .Now , the numbers of ways in which no two black balls put together is equal to the number of ways of choosing 3 places marked `"'___'"` out of eight places.
W_W_W_W_W_W_W
This can be done in `""^8C_3` ways.
`therefore` Required probability `=(""^8C_3)/(""^(10)C_3)=(8xx7xx6)/(10xx9xx8)=7/15`