Question

From a pack of 52 playing cards, three cards are drawn at random. The Probability of drawing a King, Queen and a jack is $\frac{4k}{5525}$.Find the value of k.

Answer 1

Here $n\left(S\right)={{}^{52}C}_3=\frac{52!}{3!\times 49!}=\frac{52\times 51\times 50}{3\times 2\times 1}=52\times 17\times 25$

$n\left(E\right)={{}^{4}C}_1.{{}^{4}C}_1.{{}^{4}C}_1=\frac{4!}{1!\times 3!}\times \frac{4!}{1!\times 3!}\times \frac{4!}{1!\times 3!}=4\times 4\times 4$

$\Rightarrow P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}=\frac{4\times 4\times 4}{52\times 17\times 25}=\frac{16}{5525}$
$\therefore k=4$