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

From a pack of 52 cards, 4 cards can be drawn in ${}^{52}{C}_4$ ways.
There are 13 cards of diamond and 13 cards of spades
Now 3 cards of diamond out of 13 cards of diamond can be drawn in ${}^{13}{C}_3$ ways and 1 card of spade out of 13 cards of spade can be drawn in ${}^{13}{C}_1$ ways.
Thus the probability of obtaining 3 diamond and 1 spade card
$=\frac{{}^{13}{C}_3{\times }^{13}{C}_1}{{}^{52}{C}_4}$