Poker Cards - Probability

107
0
1. The problem statement, all variables and given/known data
A gin hand consists of 10 cards from a deck of 48 cards (4 Ace Cards are missing).

Find the probability that a gin hand has all 10 cards from two suits.


2. Relevant equations



3. The attempt at a solution

So my thinking would be since we have 12 cards per suit and we are picking from two out of four possible suits, so Probability = ( 24 pick 10 ) * (4 pick 2) / (48 pick 10 )

In the actual answer there is another factor that I'm missing: (4 pick 2) [ (24 pick 10) - (2 pick 1)*(12 pick 10) ] / ( 48 pick 10)

Does anyone know where this extra term comes from? (2 pick 1)*(12 pick 10)
 
If you write (24 pick 10), then you haven't eliminated the possibility that those 10 cards come from the same suit. I think that they want you to find the probability such that the 10 cards come from two suits (and not all from 1 suit), at least thats how I interpreted the question...
 

The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top