Posted by Jay on Friday, July 20, 2012 at 1:32am.
From a deck of 52 playing cards, 7 cards are dealt. What are the odds of the following event occuring
4 From one suit, 3 from another
The probability of the event occurring is also acceptable. But, the answer is 99/16722971 (as far as the odds go

PreCalc, Probability  Reiny, Friday, July 20, 2012 at 9:18am
Could be:
HHHHCCC
HHHHSSS
HHHHDDD
Now, each of those can be arranged in 7!/(4!3!) or 35 ways
let' calculate the prob of one of these, HHHHCCC
Prob(HHHHCCC)
= (13/52)(12/51)(11/50)(10/49)(13/48)(12/47)(11/46)
But the same prob is true for all of the 35 cases,
so multiply that by 35 to get
prob(4from one suit, 3 from another) = 1573/1029112
so the prob of NOT any of those = 1  1573/1029112
= 1027539/1029112
So the odds in favour of 4 from one suit, 3 from another
= 1573 : 1027539
check my arithmetic, I did not get the same answer you gave.

ARGGHH  error PreCalc, Probability  Reiny, Friday, July 20, 2012 at 9:36am
oops, for some reason I read it as
4 Hearts, 3 from another
so it could be
HHHHCCC
HHHHSSS
HHHHDDD
DDDDHHH
DDDDCCC
DDDDSSS
SSSSHHH
SSSSCCC
SSSSDDD
CCCCHHH
CCCCSSS
CCCCDDD
So there are 12 of these and each can be arranged in 35 ways
so to get the prob of one of these 420 cases, multiply
(13/52)(12/51)(11/50)(10/49)(13/48)(12/47)(11/46) by 420
(my calculator is overheating)
Answer This Question
Related Questions
 Probability  A player is randomly dealt a sequence of 13 cards from a standard...
 Probability  An ordinary deck of playing cards has 4 suits, with 13 cards of ...
 Probability  A player is randomly dealt a sequence of 13 cards from a standard ...
 math  Three cards are selected at random without replacement from a well...
 Math  Question: You are randomly dealt 5 cards from a standard deck of 52 ...
 Math (Probability)  A standard deck of cards contains 52 cards. Of these cards ...
 math  two cards are selected at random without replacement from a wellshuffled...
 PreCalc  Five cards are dealt from a standard deck of 52 cards. What is the ...
 probability  consider the experiment of selecting a card from an ordinary deck ...
 Probability/Combinatorics  If 4 cards are drawn at random from a standard deck ...
More Related Questions