document.write( "Question 1201071: 123 year 11 students chose the courses they wanted at the school prom dinner. 75 chose a starter, 106 chose a main course and 81 chose a dessert. 67 chose a main course and dessert, 64 chose a starter and a main course while 49 chose a starter and dessert. Everybody ordered at least one course. Find the probability that a student chosen at random chose all three courses \n" ); document.write( "

Algebra.Com's Answer #835331 by ikleyn(52787) $\"\"$ $\"About$

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\n" ); document.write( "123 (\"year-11\") students chose the courses they wanted at the school prom dinner.
\n" ); document.write( "75 chose a starter, 106 chose a main course and 81 chose a dessert.
\n" ); document.write( "67 chose a main course and dessert,
\n" ); document.write( "64 chose a starter and a main course
\n" ); document.write( "while 49 chose a starter and dessert.
\n" ); document.write( "Everybody ordered at least one course.
\n" ); document.write( "Find the probability that a student chosen at random chose all three courses
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document.write( "The number of all students who chose all three cources is\r\n" );
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document.write( "    123 - (75 + 106 + 81 - 67 - 64 -49) = 41\r\n" );
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document.write( "according to the Inclusion-Exclusion principle.\r\n" );
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document.write( "Therefore, the probability that a student chosen at random chose all three courses is\r\n" );
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document.write( "     = .    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "On inclusion-exclusion principle, see this Wikipedia article\r
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\n" ); document.write( "\n" ); document.write( "https://en.wikipedia.org/wiki/Inclusion%E2%80%93exclusion_principle\r
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\n" ); document.write( "\n" ); document.write( "To see many other similar (and different) solved problems, see the lessons\r
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\n" ); document.write( "\n" ); document.write( "    - Counting elements in sub-sets of a given finite set\r
\n" ); document.write( "\n" ); document.write( "    - Advanced problems on counting elements in sub-sets of a given finite set\r
\n" ); document.write( "\n" ); document.write( "    - Challenging problems on counting elements in subsets of a given finite set \r
\n" ); document.write( "\n" ); document.write( "    - Selected problems on counting elements in subsets of a given finite set \r
\n" ); document.write( "\n" ); document.write( "    - Inclusion-Exclusion principle problems \r
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\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Happy learning (!)\r
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