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<p><strong>Cards</strong></p> <p>You are dealt a hand of five cards from a standard deck of playing cards. Find the probability of being dealt a hand consisting of:</p> <ol> <li>four-of-a-kind.<br />{2:SA:\*~=\#sola}<br /><br /></li> <li>a full house which consists of 1 three-of-a-kind and 1 two-of-a-kind.<br />{2:SA:\*~=\#solb}<br /><br /></li> <li>three-of-a-kind. (The other cards are different from each other.)<br />{2:SA:\*~=\#solc}<br /><br /></li> <li>two clubs and one of each other suits.<br />{2:SA:\*~=\#sold}</li> </ol>
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<ol> <li>«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mfenced»«mmultiscripts»«mi»C«/mi»«mn»1«/mn»«none/»«mprescripts/»«mn»13«/mn»«none/»«/mmultiscripts»«/mfenced»«mfenced»«mmultiscripts»«mi»C«/mi»«mn»4«/mn»«none/»«mprescripts/»«mn»4«/mn»«none/»«/mmultiscripts»«/mfenced»«mfenced»«mmultiscripts»«mi»C«/mi»«mn»1«/mn»«none/»«mprescripts/»«mn»12«/mn»«none/»«/mmultiscripts»«/mfenced»«mfenced»«mmultiscripts»«mi»C«/mi»«mn»1«/mn»«none/»«mprescripts/»«mn»4«/mn»«none/»«/mmultiscripts»«/mfenced»«/mrow»«mmultiscripts»«mi»C«/mi»«mn»5«/mn»«none/»«mprescripts/»«mn»52«/mn»«none/»«/mmultiscripts»«/mfrac»«/math»</li> <li>«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mfenced»«mmultiscripts»«mi»C«/mi»«mn»1«/mn»«none/»«mprescripts/»«mn»13«/mn»«none/»«/mmultiscripts»«/mfenced»«mfenced»«mmultiscripts»«mi»C«/mi»«mn»3«/mn»«none/»«mprescripts/»«mn»4«/mn»«none/»«/mmultiscripts»«/mfenced»«mfenced»«mmultiscripts»«mi»C«/mi»«mn»1«/mn»«none/»«mprescripts/»«mn»12«/mn»«none/»«/mmultiscripts»«/mfenced»«mfenced»«mmultiscripts»«mi»C«/mi»«mn»2«/mn»«none/»«mprescripts/»«mn»4«/mn»«none/»«/mmultiscripts»«/mfenced»«/mrow»«mmultiscripts»«mi»C«/mi»«mn»5«/mn»«none/»«mprescripts/»«mn»52«/mn»«none/»«/mmultiscripts»«/mfrac»«/math»</li> <li>«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mfenced»«mmultiscripts»«mi»C«/mi»«mn»1«/mn»«none/»«mprescripts/»«mn»13«/mn»«none/»«/mmultiscripts»«/mfenced»«mfenced»«mmultiscripts»«mi»C«/mi»«mn»3«/mn»«none/»«mprescripts/»«mn»4«/mn»«none/»«/mmultiscripts»«/mfenced»«mfenced»«mmultiscripts»«mi»C«/mi»«mn»2«/mn»«none/»«mprescripts/»«mn»12«/mn»«none/»«/mmultiscripts»«/mfenced»«mfenced»«mmultiscripts»«mi»C«/mi»«mn»1«/mn»«none/»«mprescripts/»«mn»4«/mn»«none/»«/mmultiscripts»«/mfenced»«mfenced»«mmultiscripts»«mi»C«/mi»«mn»1«/mn»«none/»«mprescripts/»«mn»4«/mn»«none/»«/mmultiscripts»«/mfenced»«/mrow»«mmultiscripts»«mi»C«/mi»«mn»5«/mn»«none/»«mprescripts/»«mn»52«/mn»«none/»«/mmultiscripts»«/mfrac»«/math»</li> <li>«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mfenced»«mmultiscripts»«mi»C«/mi»«mn»2«/mn»«none/»«mprescripts/»«mn»13«/mn»«none/»«/mmultiscripts»«/mfenced»«mfenced»«mmultiscripts»«mi»C«/mi»«mn»1«/mn»«none/»«mprescripts/»«mn»13«/mn»«none/»«/mmultiscripts»«/mfenced»«mfenced»«mmultiscripts»«mi»C«/mi»«mn»1«/mn»«none/»«mprescripts/»«mn»13«/mn»«none/»«/mmultiscripts»«/mfenced»«mfenced»«mmultiscripts»«mi»C«/mi»«mn»1«/mn»«none/»«mprescripts/»«mn»13«/mn»«none/»«/mmultiscripts»«/mfenced»«/mrow»«mmultiscripts»«mi»C«/mi»«mn»5«/mn»«none/»«mprescripts/»«mn»52«/mn»«none/»«/mmultiscripts»«/mfrac»«/math»</li> </ol>
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