Question

From a pack of 52 playing cards, four cards are drawn at random. find the probability of drawing all the four cards of the same suit. select one:

Answer 1

There are 4 suits in a standard deck 52 cards.
Number of ways of selecting 4 cards out of 26 cards( i.e. a suit) are

26!/(4!22!)
Note that we can choose 4 cards out of any 4 possible suits.
So total ways become:

P = 4 * ( 26!/(4!22!))

Also, no of ways to select 4 cards out of 52 cards are:

Q = 52!/(4!48!)

Hence The probability is:

P/Q

= (4*26!4!48!)/(4!22!52!)

= 0.22088835534