Question

$4$ cards are drawn from a well-shuffled deck of $52$ cards. What is the probability of obtaining $3$ diamonds and one spade?

Answer 1

Number of ways of drawing $4$ cards from $52$ cards = ${}^{52}{C}_4$
In a deck of $52$ cards there are $13$ diamonds and $13$ spades.
$\therefore$ Number of ways of drawing $3$ diamonds and one spade = ${}^{13}{C}_3{\times }^{13}{C}_1$
Thus the probability of obtaining $3$ diamonds and one spade = $\frac{{}^{13}{C}_3{\times }^{13}{C}_1}{{}^{52}{C}_4}$