Question

If two cards are selected at random from a standard deck of $52$ cards, what is the probability that they will both be diamonds?

• A. $\frac{1}{13}$
• B. $\frac{1}{4}$
• C. $\frac{1}{17}$
• D. None of these

Answer 1

The correct option is C $\frac{1}{17}$

The number of ways we can select $2$ cards from a deck of $52$ cards is ${{}^{52}C}_2=51\times 26$
The number of ways we can select $2$ cards such that they are diamonds is ${{}^{13}C}_2=13\times 6$
Probability is $\frac{13\times 6}{51\times 26}=\frac{3}{51}=\frac{1}{17}$