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,(iv)       two are red cards and two are black cards,(v)        cards are of the same colour?

Answer 1

(i) `4.^13C_4`
(ii) `.^13C_1.^13C_1.^13C_1.^13C_1`
`= 13^4`
(iii) `.^12C_4`
(iv) `.^26C_2.^26C_2`
(v) `.^26C_4*2`
answer