From a pack of 52 cards, 3 cards are selected at random. What is the probability of getting more number of kings than queens?

Question

anonymous · Answer

52C3=52*51*50/2*3=22100

anonymous · Answer

4C2*4c1*44c0/52 C3=6*4/22100

anonymous · Answer

or else (4c1*4c0*44c1+4c2*4c1*44c0+4c3*44c0*4c0)/52c3

anonymous · Answer

@ganeshie8

anonymous · Answer

or else 4/52*3/51*4/50+4/52*3/51*2/50

ganeshie8 · Answer

lets see the possible cases first

ganeshie8 · Answer

case 1 :  `1 king`,  2 others
case 2a :  `2 king`,  1 others
case 2b :  `2 king`,  `1 queen`
case 3 :  `3 kings`

ganeshie8 · Answer

In all the above cases, kings are more than queens, yes ?

anonymous · Answer

yes

anonymous · Answer

(48c2*4c1+4c2*48c1+4c2*4c1+4c3)/52c3

ganeshie8 · Answer

careful, in the first case you should not include queens

ganeshie8 · Answer

kings = 4
queens = 4
others  = 44
-----------------------
total = 52

anonymous · Answer

okay

ganeshie8 · Answer

case 1 :  `1 king`,  2 others     :  $4C1*44C2$
case 2a :  `2 king`,  1 others     :  $4C2*44C1$
case 2b :  `2 king`,  `1 queen`   :  $4C2*4C1$
case 3 :  `3 kings`                 :  $4C3$

ganeshie8 · Answer

add them all up to get the number of favorable outcomes

anonymous · Answer

4076/22100

ganeshie8 · Answer

Correct !

anonymous · Answer

(4c1*4c0*44c1+4c2*4c1*44c0+4c3*44c0*4c0)/52c3

ganeshie8 · Answer

you mean this :

( `4c1*4c0*44c2` + `4c2*4c0*44c1` + `4c2*4c1*44c0` + `4c3*44c0*4c0`)/52c3

right ?

anonymous · Answer

4096/5203,4076/5203,1024/5203,2048/5203,36/5203

anonymous · Answer

options  are:4096/5203,4076/5203,1024/5203,2048/5203,36/5203

ganeshie8 · Answer

your options are wrong, i worked this question few months back... let me see if i can find the question with correct options

anonymous · Answer

i think wrong options are given

ganeshie8 · Answer

here is the question with correct options : http://www.stepsedu.com/discuss/ans/6721/3-cards-selected-random-from-pack-52-cardswhat-probability-getting-number-kings-queens

anonymous · Answer

okay.3q .u r right.:-)

anonymous · Answer

i am so confused with options so tried to get denominator 5203.3q

anonymous · Answer

i am clear now

ganeshie8 · Answer

ikr... i had spent 1 fully day on and off on this problem before realizing that the options were wrong by googling haha

anonymous · Answer

haha...........