Question

What is the number of ways of choosing 4 cards from a pack of 52 playing cards? In how many of these
cards are of the same colour?

Answer 1

Red = 26

Black = 26

No. of cards to be chosen,4

Since, choosing red OR black

they are different cases,

So, we add the number of ways.

Total number of ways selecting four cards of

Same colour $=26C_4+26C_4$

$=2\left(26C_4\right)$

$=2\times \frac{26!}{4!(26-4)!}$

$=2\times \frac{26\times 25\times 24\times 23\times 22!}{4\times 3\times 2\times 1\times 22!}$

$=2\times \frac{26\times 25\times 24\times 23}{4\times 3\times 2\times 1}$

$=2\times 13\times 25\times 23\times 2$

$=29,900$

$\therefore$ Total no. of ways selecting four cards are of same colour $=29,900.$