Four cards are drawn at random from a pack of 52 playing cards. Find the probability of getting all the four cards of the same suit.

Answer: Option D

Four cards can be selected from 52 cards in $${}^{52}{C}_4$$ ways.
Now, there are four suits, e.g. club, spade, heart and diamond each of 13 cards.
So total number of ways of getting all the four cards of the same suit:
$$\begin{array}{rl}& {\Rightarrow }^{13}{C}_4{+}^{13}{C}_4{+}^{13}{C}_4{+}^{13}{C}_4\\ & =4{\times }^{13}{C}_4\end{array}$$
So required probability,
$$\begin{array}{rl}& =\frac{4{\times }^{13}{C}_4}{{}^{52}{C}_4}\\ & =\frac{44}{4165}\end{array}$$