Question

Two cards are drawn at random from a pack of $52$ cards. The probability that both are the cards of the spade is

• A. $\frac{1}{26}$
• B. $\frac{1}{4}$
• C. $\frac{1}{17}$
• D. None of these

Answer 1

The correct option is C

$\frac{1}{17}$

Find the required probability:

In the question, it is given that two cards are drawn at random from a pack of $52$ cards.

We know that there are $13$ cards of spade.

So, the total number of ways of selecting two cards out of $13$ cards is ${}^{13}C_2$.

And the total number of ways of selecting two cards out of $52$ cards is ${}^{52}C_2$.

So, the required probability is given by $\frac{{}^{13}C_2}{{}^{52}C_2}=\frac{13\times 12}{52\times 51}$.

Therefore, the required probability is $\frac{1}{17}$.

Hence, option (C) is the correct option.