Question

Six cards are drawn simultaneously from a pack of playing cards. What is the probability that $3$ will be red and $3$ black

• A. ${}^{26}C_6$
• B. $\frac{{}^{26}C_3}{{}^{52}C_6}$
• C. $\frac{{}^{26}C_3·{}^{26}C_3}{{}^{52}C_6}$
• D. $\frac{1}{2}$

Answer 1

The correct option is C

$\frac{{}^{26}C_3·{}^{26}C_3}{{}^{52}C_6}$

Explanation for the correct answer:

Finding the probability that three cards will be red and three cards will be black:

Total number of cards $=52$

Three red cards $+$ three black cards $=6$

Total cases ${=}^{52}{C}_6$

We know that, out of $52$ cards, $26$ cards are red and $26$ cards are black.

Hence, favourable cases${=}^{26}{C}_3{·}^{26}{C}_3$

Hence, the required probability $=\frac{\text{favourable cases}}{\text{total cases}}$

$=\frac{{}^{26}C_3.{}^{26}C_3}{{}^{52}C_6}$

Therefore, option (C) is the correct answer.