Question

What is the number of ways of choosing $4$ cards from a pack of $52$ playing cards? In how many of these two are red cards and two are black cards.

Answer 1

Black .$26$

Red .$26$

No of cards chosen 2 from each colour

since, they are the same case,

so,we multipy the number of ways

Total no.of ways choosing 2 red & black cards =$26C_2\times 26C_2$

$=(26C_2{)}^2$

$=(\frac{26!}{2!(26-2)!}{)}^2$

$=(\frac{26!}{2!.24!}{)}^2$

$=(\frac{26\times 25\times 24!}{2\times 24!}{)}^2$

$=(13\times 25{)}^2$

$=(325{)}^2$

$=105625$

$\therefore$Total no.of ways choosing 2red and black cards

are $105625$ ways.