Question

$A$ and $B$ draw two cards one after other from a pack of $52$ cards. The probability that all four cards of same colour is

• A. $\frac{1}{17 \times7}$
• B. $\frac{46}{49 \times17}$
• C. $\frac{92}{49 \times17}$
• D. None of these

Answer 1

Answer: (C)

$n\left(A\right) =$ Number of ways of drawing $4$ cards of same colour
$= \,{}^{2}C_{1} \times \,{}^{26}C_{2} \times \,{}^{24}C_{2}$
$n\left(S\right) = \,{}^{52}C_{2} \times \,{}^{50}C_{2}$
$\therefore $ Required probability$=\frac{\,{}^{26}C_{2} \times \,{}^{24}C_{2} \times2}{\,{}^{52}C_{2} \times \,{}^{50}C_{2}} = \frac{92}{49 \times17}$