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. $\frac{1}{2}$
• B. $\frac{7}{15}$
• C. $\frac{2}{15}$
• D. $\frac{1}{3}$

Answer 1

The correct option is B $\frac{7}{15}$

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 gaps
To choose 3 out of 8 gaps ${}^8{C}_3$ ways
Probability = $\frac{8favourable}{Total}$
= $\frac{{}^8{C}_3}{{}^{10}{C}_3}$
= $\frac{8!3!7!}{3!5!10!}=\frac{6\times 7}{9\times 10}=\frac{7}{15}$