Question

A bag contains $8$ red and $5$ white balls. Three balls are drawn at random. The probability that one ball is red and two balls are white is $\frac{10k}{143}$. What is the value of $k$?

Answer 1

P(one ball is red and two balls are white) $=\frac{{}^8{C}_1{\times }^5{C}_2}{{}^{13}{C}_3}$

$=\frac{8\times 10}{\frac{13\times 12\times 11}{6}}=\frac{40}{143}$

$k=10$