Question

A bag contains $5$ white$,$ $7$ black$,$ and $4$ red balls$:$ find the chance that three balls drawn at random are all white.

Answer 1

Total number of balls $=5+7+4=16$

Total number of ways in which three balls can be drawn ${=}^{16}{C}_3=\frac{16!}{(16-3)!3!}=\frac{16!}{13!3!}=560$

Total number of white balls $=5$

Number of ways in which three white balls can be drawn ${=}^5{C}_3=\frac{5!}{(5-3)!3!}=\frac{5!}{2!3!}=10$

$\therefore$ required probability $=\frac{10}{560}=\frac{1}{56}$