document.write( "Question 1203989: A lottery exists where balls numbered 1 to 18 are placed in an urn. Five balls are randomly selected. To​ win you must match all five balls in any order. How many possible outcomes are there for this​ game? \n" ); document.write( "
Algebra.Com's Answer #839958 by math_tutor2020(3816)\"\" \"About 
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\n" ); document.write( "Answer: 8568\r
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\n" ); document.write( "\n" ); document.write( "Work Shown:\r
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\n" ); document.write( "\n" ); document.write( "n = 18 balls total
\n" ); document.write( "r = 5 selections\r
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\n" ); document.write( "\n" ); document.write( "Order doesn't matter, so we use the nCr combination formula.
\n" ); document.write( "n C r = (n!)/(r!(n-r)!)
\n" ); document.write( "18 C 5 = (18!)/(5!*(18-5)!)
\n" ); document.write( "18 C 5 = (18!)/(5!*13!)
\n" ); document.write( "18 C 5 = (18*17*16*15*14*13!)/(5!*13!)
\n" ); document.write( "18 C 5 = (18*17*16*15*14)/(5!)
\n" ); document.write( "18 C 5 = (18*17*16*15*14)/(5*4*3*2*1)
\n" ); document.write( "18 C 5 = 1028160/120
\n" ); document.write( "18 C 5 = 8568\r
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\n" ); document.write( "\n" ); document.write( "Another approach:\r
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\n" ); document.write( "\n" ); document.write( "There are 18*17*16*15*14 = 1028160 permutations possible. Start at 18 and count down until we fill 5 slots.
\n" ); document.write( "Divide that permutation by 5! = 5*4*3*2*1 = 120 to correct for over-counting.
\n" ); document.write( "For instance, the set {1,2,3,4,5} is the same as {1,3,2,4,5} since order doesn't matter. There are 120 ways to arrange any set of five items.
\n" ); document.write( "This is how we arrive at 1028160/120 = 8568 different ways to play the game.
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