document.write( "Question 1162132: For a community service project, 10 students volunteer to do some cleaning up at an old folk’s home. The teacher in charge wants to split them up in 3 groups. One group will consist of 5 students in clean the rooms; another group of 3 students to clean the toilets; the last group of 2 students to sweep the corridors. Find the number of ways the teacher in charge can form the groups. \n" ); document.write( "

Algebra.Com's Answer #785850 by Edwin McCravy(20060) $\"\"$ $\"About$

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For a community service project, 10 students volunteer to do some cleaning
\n" ); document.write( "up at an old folk’s home. The teacher in charge wants to split them up in 3
\n" ); document.write( "groups. One group will consist of 5 students in clean the rooms; another
\n" ); document.write( "group of 3 students to clean the toilets; the last group of 2 students to
\n" ); document.write( "sweep the corridors. Find the number of ways the teacher in charge can form
\n" ); document.write( "the groups.
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document.write( "For the rooms, 10 students CHOOSE 5.  That's 10C5 = 252 ways\r\n" );
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document.write( "For each of those 252 ways, we have for the toilets, \r\n" );
document.write( "5 remaining students CHOOSE 3. That's 5C3 = 10 ways.\r\n" );
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document.write( "So there are 252∙10=2520 ways to choose the room crew and toilet crew\r\n" );
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document.write( "For each of those 2520 ways, we have for the corridor crew, \r\n" );
document.write( "2 remaining students CHOOSE both 2. That's 2C2 = 1 way\r\n" );
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document.write( "Answer: 252∙10∙1 = 2520 ways the teacher can form the three groups.\r\n" );
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document.write( "Edwin

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