PreCalc, Probability
posted by Jay .
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

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. 
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)
Respond to this Question
Similar Questions

Math
Question: You are randomly dealt 5 cards from a standard deck of 52 playing cards. What is the probability that you have at least 4 cards of the same suit? 
probability
consider the experiment of selecting a card from an ordinary deck of 52 playing cards and determine the probability of the stated event. A card that is not a king and not a spade is drawn. I know there are 52 cards in a deck and there … 
Probability
A player is randomly dealt a sequence of 13 cards from a standard 52card deck. All sequences of 13 cards are equally likely. In an equivalent model, the cards are chosen and dealt one at a time. When choosing a card, the dealer is … 
Probability
A player is randomly dealt a sequence of 13 cards from a standard 52card deck. All sequences of 13 cards are equally likely. In an equivalent model, the cards are chosen and dealt one at a time. When choosing a card, the dealer is … 
Probability
An ordinary deck of playing cards has 4 suits, with 13 cards of each suit. In many games, each of 4 players is dealt 13 cards at random. a. What is the probability that such a hand has each of the following? 
math
two cards are selected at random without replacement from a wellshuffled deck of 52 playing cards. find the probability of the given event. a. two cards of the same suit are drawn. b. a pair is not drawn. 
Math (Probability)
A standard deck of cards contains 52 cards. Of these cards there are 13 of each type of suit (hearts, spades, clubs, diamonds) and 4 of each type of rank (A – K). Two cards are pulled in order, without replacement from this deck … 
math
Three cards are selected at random without replacement from a wellshuffled deck of 52 playing cards. Find the probability of the given event. (Round your answer to four decimal places.) Three cards of the same suit are drawn 
PreCalc
Five cards are dealt from a standard deck of 52 cards. What is the probability that three or four of the cards are aces? 
math
A standard deck of cards has 52 cards in it. The cards are divided into 4 suits or 13 cards each.If one draws two cards at random from the deck of cards what is the probability that they are of the same suit ?