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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...

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1 Answer

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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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