document.write( "Question 385820: Allen is in the Boy Scouts. He has three weeks left in which to complete the hours required for a merit badge in community service. Because of his paper route and homework, he can't put in more than 5 hours in any one week for the merit badge. How many different ways can Allen work a total of 10 hours over the three week period? So far I have 23 different combinations. I am wondering if that is the total or if there is more. \n" ); document.write( "

Algebra.Com's Answer #273265 by sudhanshu_kmr(1152) $\"\"$ $\"About$

You can put this solution on YOUR website!
10 hours can be sum of either of these set (according to question)...\r
\n" ); document.write( "\n" ); document.write( "( 5,5,0 ), (5,1,4), (5,2,3), (4,2,4) and (4,3,3)\r
\n" ); document.write( "\n" ); document.write( "now,\r
\n" ); document.write( "\n" ); document.write( "(5,5,0) can be arrange in 3 weeks by 3!/2! ways = 3\r
\n" ); document.write( "\n" ); document.write( "similarly, for(5,1,4)............ ....by 3! ways = 6 \r
\n" ); document.write( "\n" ); document.write( "......for (5,2,3) ........................ 3! ways = 6
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\n" ); document.write( "......for (4,2,4).......................3!/2! ways = 3\r
\n" ); document.write( "\n" ); document.write( " .....for (4,3,3)........................3!/2! ways = 3\r
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\n" ); document.write( "\n" ); document.write( "total no. of ways.................................= 21 (sum of above)\r
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\n" ); document.write( "\n" ); document.write( "so, total 21 ways......\r
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