If three cards are chosen at random from a standard deck of playing cards, how many different ways are there to draw the three cards if at least two cards are a jack, queen or a king?
Whats the answer and how?
Probability Question
This topic has expert replies
-
- Legendary Member
- Posts: 559
- Joined: Tue Mar 27, 2007 1:29 am
- Thanked: 5 times
- Followed by:2 members
If three cards are chosen at random from a standard deck of playing cards, how many different ways are there to draw the three cards if at least two cards are a jack, queen or a king?
Total cards in a deck = 52(13 of each of the 4 types)
Total kings =4
Total queens = 4
Total jacks =4
4+4+4 = 12
Now there are 2 possibilities
1) 2 cards are either a king,queen or a king
2) All 3 cards drawn are either a king,queen or jack
1) 12C2*40C1 = 6*11*40 = 2640
2) 12C3 = 2*10*11 = 220
Hence total = 2640+220 = 2860
Total cards in a deck = 52(13 of each of the 4 types)
Total kings =4
Total queens = 4
Total jacks =4
4+4+4 = 12
Now there are 2 possibilities
1) 2 cards are either a king,queen or a king
2) All 3 cards drawn are either a king,queen or jack
1) 12C2*40C1 = 6*11*40 = 2640
2) 12C3 = 2*10*11 = 220
Hence total = 2640+220 = 2860
- jayhawk2001
- Community Manager
- Posts: 789
- Joined: Sun Jan 28, 2007 3:51 pm
- Location: Silicon valley, California
- Thanked: 30 times
- Followed by:1 members
I have general question here. Given that we are asked to find theCybermusings wrote: If three cards are chosen at random from a standard deck of playing cards, how many different ways are there to draw the three cards if at least two cards are a jack, queen or a king?
Now there are 2 possibilities
1) 2 cards are either a king,queen or a king
2) All 3 cards drawn are either a king,queen or jack
1) 12C2*40C1 = 6*11*40 = 2640
2) 12C3 = 2*10*11 = 220
Hence total = 2640+220 = 2860
total number of ways in which the cards can be chosen, is it correct
to use 12C2 -- shouldn't it be 12P2, since say KQ2 and QK2 are
different ways of "drawing" the 3 cards.
More specifically, going by how the draw takes place --
Prob of choosing 2 paint-cards = 12 * 11 * 40 (which is the same as 12P2 * 40)
Can someone please confirm.