Question

In a bag there are $N$ balls out of which $R$ are red.If $n$ balls are drawn at random from the bag, the probability that $r$ of them are red is

• A. $\frac{n_{C_r}}{{}^N{C}_n}$
• B. $\frac{R_{C_r}}{{}^N{C}_n}$
• C. $\frac{{}^R{C}_r{\times }^{N-R}{c}_{n-r}}{{}^N{C}_n}$
• D. $\frac{{}^N{C}_r}{{}^R{C}_n}$

Answer 1

The correct option is C $\frac{{}^R{C}_r{\times }^{N-R}{c}_{n-r}}{{}^N{C}_n}$

We need to select $r$ red out of $R$ red balls and $n-r$ non-red balls out of $N-R$ non-red balls.
Hence, probability = $\frac{{}^R{C}_r{\ast }^{N-R}{C}_{n-r}}{{}_n^{N}C}$