Question

A bag contains 8 red and 5 white balls. Three balls are drawn at random. The probability that all the three balls are white is $\frac{5k}{286}$.Then find the value of $k$

Answer 1

Probability of all 3 balls being white$=P\left(w_1\right)P\left(w_2\right)P\left(w_3\right)=\left(\frac{5}{8+5}\right)\left(\frac{4}{8+4}\right)\left(\frac{3}{8+3}\right)=\frac{60}{1716}=\frac{10}{286}$
Hence $k=\frac{10}{5}=2$.