Question

$4$ cards are chosen from a pack of $52$ playing cards?

In how many of these two are red cards and two are black cards.

Answer 1

Numbers of ways of choosing $4$ cards is ${}^{52}{C}_4$

There are $26$ red cards and $26$ black cards

Since, there are 2 red cards and 2 black cards to be chosen
$\therefore$ no. of ways in which red card is chosen=${}^{26}{C}_2$

no. of ways in which black card is chosen =${}^{26}{C}_2$

$\therefore$ Numbers of ways is ${}^{26}{C}_2{\times }^{26}{C}_2=(325{)}^2$