How Many Bridge Hands Include Specific Card Suits?

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The discussion focuses on calculating the number of possible bridge hands that include five spades, three diamonds, three clubs, and two hearts. The initial calculations incorrectly add the combinations of each suit, resulting in a total of 1,937 hands. The correct approach involves multiplying the combinations for each suit: 13C5 for spades, 13C3 for diamonds, 13C3 for clubs, and 13C2 for hearts. This multiplication yields the accurate total of 8,211,173,256 possible hands. The key takeaway is to use multiplication rather than addition for determining the total combinations in this scenario.
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Homework Statement

How many different bridge hands are possible containing five spaids, three diamonds, three clubs, and two hearts?




Homework Equations





The Attempt at a Solution


Total number of hands in which I can get 5 spaids is 13C5
Total number of hands in which I can get 3 diamonds is 13C3
Total number of hands in which I can get 3 clubs is 13C3
Total number of hands in which I can get 2 hearts is 13C2
Adding these up gives 1937 which is not any where close to 8,211,173,256.
Help?
 
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stevecallaway said:

Homework Statement

How many different bridge hands are possible containing five spaids, three diamonds, three clubs, and two hearts?
Those would be "spades."
stevecallaway said:

Homework Equations





The Attempt at a Solution


Total number of hands in which I can get 5 spaids is 13C5
Total number of hands in which I can get 3 diamonds is 13C3
Total number of hands in which I can get 3 clubs is 13C3
Total number of hands in which I can get 2 hearts is 13C2
Adding these up gives 1937 which is not any where close to 8,211,173,256.
Help?

Multiply all four numbers together and you get the right result.
 
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Thread 'Confusion regarding a chemical kinetics problem'

TL;DR Summary: cannot find out error in solution proposed. [![question with rate laws][1]][1] Now the rate law for the reaction (i.e reaction rate) can be written as: $$ R= k[N_2O_5] $$ my main question is, WHAT is this reaction equal to? what I mean here is, whether $$k[N_2O_5]= -d[N_2O_5]/dt$$ or is it $$k[N_2O_5]= -1/2 \frac{d}{dt} [N_2O_5] $$ ? The latter seems to be more apt, as the reaction rate must be -1/2 (disappearance rate of N2O5), which adheres to the stoichiometry of the...
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