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7 white balls and 3 black balls are kept...

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)/(12)`

C

`(2)/(15)`

D

`(1)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
B
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`
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