Question

Four cards are drawn at random from a pack of 52 playing cards. Find the probability of getting 1.) 4 cards of the same suit 2.) One card from each suit 3.) Two red and two black cards

Answer 1

favorable outcome`=13C_4*4`
Total outcome=`52C_4`
`P=(13C_4*4)/(52C_4)`
`P=(12*11)/(51*5*49)`
`P=(52C_1)/(52C_1)*(26C_1)/(51C_1)*(26C_!)/(50C_1)*(13C_1)/(49C_1)`
`P=1*39/51*26/50*13/49`
`P=(13)^3/(17*25*49)`
`P=(26C_2)/(52C_2)*(26C_2)/(50C_2)`
`P=(25*26)^2/(45*50*51*52)`.