From a bag containing 4 white and 5 black balls a man drawn 3 balls at random. What are the odds against these balls being black?

Answer: Option B

Probability of all three balls being black
$$\begin{array}{rl}& =\frac{{}^5{C}_3}{{}^9{C}_3}\\ & =\frac{5}{42}\end{array}$$
Probability that three balls are not black
$$\begin{array}{rl}& =1-\frac{5}{42}\\ & =\frac{37}{42}\end{array}$$
Hence, odds against these ball being black
$$\begin{array}{rl}& =\left(\frac{37}{42}\right):\left(\frac{5}{42}\right)\\ & =37:5\end{array}$$