Question

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 number.

Answer 1

The number of ways to select 4 cards from a pack of 52 cards is ${}^{52}{C}_4=\frac{\left(52\right)!}{(52-4)!4!}$
$=\frac{52\times 51\times 50\times 49\times 48!}{\left(48\right)!\times 4\times 3\times 2\times 1}$
$=270725$
Thus, total number of out comes is n(S)=270725
Since, in a pack of 52 cards, there are $13$ different numbered cards.
So, required probaility $=\frac{13}{270725}$
$=\frac{1}{20825}$