document.write( "Question 1191200: 5 Cards are drawn randomly from a regular deck of cards. How many ways can you draw 5 cards and get 4 hearts and 1 spade? \n" ); document.write( "
Algebra.Com's Answer #823009 by math_tutor2020(3817)\"\" \"About 
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\n" ); document.write( "We'll use the nCr combination formula because order doesn't matter when selecting the cards.\r
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\n" ); document.write( "\n" ); document.write( "Let's find out how many ways there are to select the four hearts
\n" ); document.write( "n = 13 hearts total
\n" ); document.write( "r = 4 to select\r
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\n" ); document.write( "\n" ); document.write( "n C r = (n!)/(r!(n-r)!)
\n" ); document.write( "13 C 4 = (13!)/(4!*(13-4)!)
\n" ); document.write( "13 C 4 = (13!)/(4!*9!)
\n" ); document.write( "13 C 4 = (13*12*11*10*9!)/(4!*9!)
\n" ); document.write( "13 C 4 = (13*12*11*10)/(4!)
\n" ); document.write( "13 C 4 = (13*12*11*10)/(4*3*2*1)
\n" ); document.write( "13 C 4 = (17160)/(24)
\n" ); document.write( "13 C 4 = 715\r
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\n" ); document.write( "\n" ); document.write( "There are 715 ways to pick the four hearts.\r
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\n" ); document.write( "\n" ); document.write( "Then there are 13C1 = 13 ways to pick the 1 spade since we have 13 spades to pick from and one slot to fill.\r
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\n" ); document.write( "\n" ); document.write( "The number of five card hands with four hearts and one spade is therefore: 715*13 = 9295
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