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.

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,
$$\eqalign{ & = \frac{{4{ \times ^{13}}{C_4}}}{{^{52}{C_4}}} \cr & = \frac{{44}}{{4165}} \cr} $$