Question

Find the number of 5 card possible hands specified:

a) all red cards

b) all hearts

c) all face cards

d) all kings

Answer 1

a) There are 26 red cards. If we pick one of them 25 remains and so on

So by multiplication rule

Number of 5 cards possible when all of them are red cards = 26*25*24*23*22 = 7893600

b) There are 13 heart cards. If we pick one of them 12 remains and so on

So by multiplication rule

Number of 5 cards possible when all of them are heart cards = 13*12*11*10*9 = 154440

c) There are 12 face cards. If we pick one of them 11 remains and so on

So by multiplication rule

Number of 5 cards possible when all of them are face cards = 12*11*10*9*8 = 95040

b) There are 4 king cards. If we pick one of them 3 remains and so on

So by multiplication rule

Number of 5 cards possible when all of them are heart cards = 4*3*2*1*48 = 1152

(48 because when all kings are picked up there are 48 cards remaining and all of them have equal probablity of picking up)