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.

A. $$\frac{{13}}{{270725}}$$

B. $$\frac{{91}}{{190}}$$

C. $$\frac{{178}}{{20825}}$$

D. $$\frac{{44}}{{4165}}$$

Answer: Option D

Solution(By Examveda Team)

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:
$$\eqalign{ & { \Rightarrow ^{13}}{C_4}{ + ^{13}}{C_4}{ + ^{13}}{C_4}{ + ^{13}}{C_4} \cr & = 4{ \times ^{13}}{C_4} \cr} $$
So required probability,
$$\eqalign{ & = \frac{{4{ \times ^{13}}{C_4}}}{{^{52}{C_4}}} \cr & = \frac{{44}}{{4165}} \cr} $$