Since 4 cards can be drawn at a time from a pack of 52 cards is ⁵²C₄ ways,
total number of elementary events = ⁵²C₄
Consider the following events:
A : Getting all spade cards;
B : Getting all club cards;
C : Getting all diamond cards;
D : Getting all hearts cards.
Then A, B, C and D are mutually exclusive events such that

$\mathrm{P}\left(\mathrm{A}\right)=\frac{{}^{13}{\mathrm{C}}_4}{{}^{52}{\mathrm{C}}_4}, \mathrm{P}\left(\mathrm{B}\right)=\frac{{}^{13}{\mathrm{C}}_4}{{}^{52}{\mathrm{C}}_4}, \mathrm{P}\left(\mathrm{C}\right)=\frac{{}^{13}{\mathrm{C}}_4}{{}^{52}{\mathrm{C}}_4}, \mathrm{P}\left(\mathrm{D}\right)=\frac{{}^{13}{\mathrm{C}}_4}{{}^{52}{\mathrm{C}}_4}$
Now required probability
= P(A⋃B⋃C⋃D)

= P(A) + P(B) + P(C) + P(D)

$=4\left(\frac{{}^{13}{\mathrm{C}}_4}{{}^{52}{\mathrm{C}}_4}\right)=\frac{44}{4165}$