Question

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

• A. $\frac{44}{4165}$
• B. $\frac{22}{4165}$
• C. $\frac{11}{4165}$
• D. None of these

Answer 1

The correct option is A $\frac{44}{4165}$

From the deck of $52$ cards, $4$ cards are to be drawn.

So total outcomes $=$ ${{}^{52}C}_4$

Now we need all four cards to be from same suit.

So we select four cards from a deck by ${{}^{13}C}_4$ ways.

And there are $4$ suits for which this can be repeated so favorable outcomes are $4\times {{}^{13}C}_4$

Thus probability, $p=\frac{4\times {{}^{13}C}_4}{{{}^{52}C}_4}=\frac{44}{4165}$