document.write( "Question 1173392: In a school, every grade 10 student need to study 7 subjects out of 14. It is given that 4 of them are core subject, and the rest are optional. How many arrangements of the subjects are available for the students? \n" ); document.write( "

Algebra.Com's Answer #850760 by ikleyn(52847) $\"\"$ $\"About$

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\n" ); document.write( "In a school, every grade 10 student need to study 7 subjects out of 14.
\n" ); document.write( "It is given that 4 of them are core subject, and the rest are optional.
\n" ); document.write( "How many arrangements of the subjects are available for the students?
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\n" ); document.write( "\n" ); document.write( "        Based on the context, my common sense says me that this problem is about combinations,\r
\n" ); document.write( "\n" ); document.write( "        and not about permutations, as @CPhill calculates and treats it.\r
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\n" ); document.write( "\n" ); document.write( "        So, I solve it differently, and my answer is different from that by @CPhill.\r
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document.write( "Every student must take 4 core subjects, and a student should take 3 additional subjects, selecting them\r\n" );
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document.write( "from  14-4 = 10 remaining optional subjects.\r\n" );
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document.write( "So, the total number of all possible combinations is   =  = 120.     ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved. The order of subjects in arrangements does not matter.\r
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\n" ); document.write( "\n" ); document.write( "I am 137% sure that the treatment by @CPhill is not that the problem does require.\r
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