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cameron

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from a deck of 52 cards, how many ways can you draw a five card hand where at least one card is a heart?

please answer! this is one problem on my probability homework that i just can't get

Posted 789 day ago

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Answers (3)

ger2000 		every 14th card

Posted 789 day ago

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fullhouse 		the negation of "at least 1 heart" is "no hearts", so

ways to draw 5-card hand - ways to draw no-heart 5-card hand =
52C5 - 39C5 =
2598960 - 575757 =
2,023,203

Posted 789 day ago

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ger2000 		This is = P{1st is H} +
P{1st not H} * P{2nd card is H/1st not} +
P{1st 2 not H} * P{3rd card is H/1st 2 not} +
P{1st 3 not H} * P{4rd card is H/1st 3 not} +
P{1st 4 not H} * P{5rd card is H/1st 4 not}
= (13/52) +
(39/52) * (13/51) +
(39/52)*(38/51)*(13/50) +
(39/52)*(38/51)*(37/50)*(13/49) +
(39/52)*(38/51)*(37/50)*(36/49)*(13/48) = 0.7784663866

The number of ways (permutations) = .7784663866 * 48*49*50*51*52=242784360

Posted 789 day ago

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Question Title from a deck of 52 cards, how many ways can you draw a five card hand where at least one card is a heart?
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