Question

# $$7$$ white balls and $$3$$ black balls are placed in a row at random. The probability that no two black balls are adjacent is

A
12
B
715
C
215
D
13

Solution

## The correct option is B $$\dfrac{7}{15}$$We will put black balls in the gaps to ensure no two block balls are adjacent 7 white balls_W_W_W_W_W_W_W_8 gapsTo choose 3 out of 8 gaps $$^8C_3$$ waysProbability = $$\frac { 8\quad favourable }{ Total }$$= $$\displaystyle \frac { ^{ 8 }{ C_{ 3 } } }{ _{ }^{ 10 }{ C_{ 3 } } }$$= $$\displaystyle \frac { 8!3!7! }{ 3!5!10! } =\frac { 6\times 7 }{ 9\times 10 } =\frac { 7 }{ 15 }$$Maths

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