Question

A bag contains $5$ white, $7$ black, and $4$red balls. Three balls are drawn from the bag at random. The probability that the three balls are white, is

• A. $3/16$
• B. $3/5$
• C. $1/60$
• D. $1/56$

Answer 1

The correct option is D

$1/56$

Explanation for correct option:

Find the Probalbiity :

$\mathbf{Probabilty}\mathbf{}\mathbf{=}\frac{\mathbf{Favourable}\mathbf{}\mathbf{cases}}{\mathbf{Total}\mathbf{}\mathbf{cases}}$

Number of white balls $=5$

Number of black balls $=7$

Number of red balls $=4$

Total number of balls $=16$

We have drawn $3$ white balls, so

Total cases $={}^{16}C_3$

Favourable cases $={}^{5}C_3$

Probability $=\frac{{}^{5}C_3}{{}^{16}C_3}$

$$\begin{gathered} =\frac{10}{560} \\ =\frac{1}{56} \end{gathered}$$

Hence, the the correct option is (D).