document.write( "Question 658817: the number of ways in which 12 mangoes can be equally divided among 3 student \n" ); document.write( "
Algebra.Com's Answer #410528 by math-vortex(648)\"\" \"About 
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Hi, there--\r
\n" ); document.write( "\n" ); document.write( "You asking for a combination---the number of ways that n objects (mangoes) can be sub-divided into groups of r objects (students). We don't care what order the objects are in. Getting mango 1, mango 2, and mango 3 would be the same as getting mango 3, mango 1, and mango 2.\r
\n" ); document.write( "\n" ); document.write( "You sometimes hear this called \"n choose r\" or, in your problem, \"12 choose 3.\" It can be written as 12C3. The formula is\r
\n" ); document.write( "\n" ); document.write( "nCr = n! / ((n-r)! * r!)\r
\n" ); document.write( "\n" ); document.write( "12C3 = 12! / ((12-3)! * 3!)
\n" ); document.write( "12C3 = 12! / (9! * 3!)\r
\n" ); document.write( "\n" ); document.write( "When you expand the factorials out, you will find that many factors cancel out. \r
\n" ); document.write( "\n" ); document.write( "12C3 = (12*11*10*9!) / (9! * 3*2*1)
\n" ); document.write( "12C3 = (12*11*10) / (3*2)
\n" ); document.write( "12C3 = 2*11*10
\n" ); document.write( "12C3 = 220\r
\n" ); document.write( "\n" ); document.write( "There 220 unique ways to divide 12 mangoes among 3 students.\r
\n" ); document.write( "\n" ); document.write( "Best,
\n" ); document.write( "Ms.Figgy
\n" ); document.write( "math.in.the.vortex@gmail.com
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