Question

The probability of having a king and a queen when the two cards are drawn at random from a pack of 52 cards is:

• A. $\frac{16}{663}$
• B. $\frac{8}{663}$
• C. $\frac{4}{663}$
• D. $\frac{2}{663}$

Answer 1

Answer: (B)

$\frac{8}{663}$

Answer 2

Number of ways of getting king alone = ${^4C_1}$ Number of ways of getting queen alone = ${^4C_1}$ Total number of ways in which 2 cards are drawn from a pack of 52 cards = ${^{52}C_2}$. $\Rightarrow$ Required probability $= \frac{^{4}C_{1} \times^{4}C_{1}}{^{52}C_{2} } = \frac{4 \times4 \times2}{52\times51} = \frac{8}{663}$