Question

Four cards are drawn at random from a well shuffled pack of $52$ cards.
Find the probability that they all are diamonds

Answer 1

$n\left(A\right)={}^{13}{C}_{4}n\left(S\right){=}^{52}{C}_4$
$P\left(A\right)=\frac{{}^{13}{C}_4}{{}^{52}{C}_4}=\frac{13\times 12\times 11\times 10}{52\times 51\times 50\times 49}=\frac{11}{4165}$
$\therefore$ the probability of drawing four cards that are diamonds $=\frac{11}{4165}$