Question

Four cards are drawn at random from a well shuffled pack of $52$ cards.
Find the probability that there are two spades and two hearts

Answer 1

$n\left(B\right){=}^{13}{C}_2{\times }^{13}{C}_{2}n\left(S\right){=}^{52}{C}_4$
$\therefore P\left(B\right)=\frac{{}^{13}{C}_2{\times }^{13}{C}_2}{{}^{52}{C}_4}=\left[\frac{\frac{13\times 12\times 13\times 12}{2\times 2}}{\frac{52\times 51\times 50\times 49}{4\times 3\times 2\times 1}}\right]=\frac{468}{20825}$
$\therefore$ the probability of drawing two spades and two hearts is $\frac{468}{20825}$