Question

A bag contains 8 red and 5 white balls. Three balls are drawn at random. Find the probability that all the three balls are red

• A. $\frac{{}^8{C}_3}{{}^{13}{C}_3}$
• B. $\frac{{}^8{C}_5}{{}^{13}{C}_3}$
• C. $\frac{28}{143}$
• D. None of the above.

Answer 1

Answer: (A), (B), (C)

$\frac{{}^8{C}_5}{{}^{13}{C}_3}$
$\frac{28}{143}$
$\frac{{}^8{C}_3}{{}^{13}{C}_3}$

Number of ways of drawing any three ball $n\left(S\right){=}^{13}{C}_3$
Number of ways of drawing three red ball $n\left(E\right){=}^8{C}_3{=}^8{C}_5$ ${\because }^n{C}_r{=}^n{C}_{n-r}$
Therefore required probability $P=\frac{n\left(E\right)}{n\left(S\right)}=\frac{{}^8{C}_3}{{}^{13}{C}_3}=\frac{{}^8{C}_5}{{}^{13}{C}_3}=\frac{28}{143}$