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 spade. 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 diamonds and 1 spade card = $\frac{{}^{13}C_3 \times {}^{13}C_1}{{}^{52}C_4}$