Choose 5 cards from a standard deck of 52. What is the chance we will have 2 face cards, 2 cards with value smaller than 6 and 1 card with value between 6 and 10 ?
Please help! Not sure how to attack this problem...
Choose 5 cards from a standard deck of 52. What is the chance we will have 2 face cards...
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probability
permutations
combinations
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2Pick which two face cards are in the hand. Pick which two cards are of value smaller than six. Pick which one card is between 6 and 10. Apply multiplication principle and divide by the number of five card hands that exist. Profit. – 2017-01-29
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0@Joffan If it was lauren that asked, I'd justify that with a full answer. You clearly already know what I'm talking about and don't need me to explain further. – 2017-01-29
1 Answers
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Find the card counts in each of your categories, and pick the requisite number from each category. See binomial coefficients for the calculation of choosing (say) 2 from 20, written $\binom{20}{2}$. Since each of these three choice calculations applies regardless of the choice made in other categories, you multiply them up. Then you just need divide by the "choose 5 from 52" $\binom{52}{5}$ overall possible hands to get the probability.
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0I ended up get (12 2)*(20 2)*(20 1) all divided by (52 5) which gave me a probability of .0609? – 2017-01-29
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0@laurenq should be $250800/2598960 \approx 0.0965$ – 2017-01-29
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0okay i see where i went wrong. Thank you – 2017-01-29