SOLUTION: If you remove all face cards from a standard deck of cards, what is the probability that you will draw a full house in a 5 card hand?

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Question 31456: If you remove all face cards from a standard deck of cards, what is the probability that you will draw a full house in a 5 card hand?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
After taking out those cards you have a deck with 40 cards
There are 10 different cards.
To figure the probability:
pick a card type: 10 ways
Now pick 3 of the 4 cards of that type: 4C3=4 ways
Pick another card type: 9 ways
Now pick 2 of the 4 card of that type: 4C2=6 ways
So, number of ways to succeed is 10*4*9*6=2160
Now figure the total number of 5 card hands in a deck of 40 cards:
40C5= 658008 different hands
Prob of a full house with the special deck = 2160/658008=0.00328...
Cheers,
Stan H.