Question

What is the number of ways of choosing $4$ cards from a pack of $52$ playing cards? In how many of these?
(i) four cards are of the same suit
(ii) four cards belong to four different suits
(iii) are face cards
(v) cards are of the same colour?
(v) two are red cards and two are black cards

Answer 1

No. of ways of choosing 4 cards from 52 = ${}^{52}{C}_4$

Now,

(a.) (4.)${}^{13}{C}_4$

(b.) ${}^{13}{C}_1$. ${}^{13}{C}_1$.${}^{13}{C}_1$.${}^{13}{C}_1$

(c.) No. of face cards $=12$ $\therefore {}^{12}{C}_4$

(d.) (2)${(}^{26}{C}_4)$

black + Red

(e.) ${}^{26}{C}_2$. ${}^{26}{C}_2$