document.write( "Question 1176466: The University of Ballygobackwards has three colleges:
\n" ); document.write( "- the College of Science, which has 19 staff, 5 of whom are female;
\n" ); document.write( "- the College of Engineering, which has 6 staff, 4 of whom are female;
\n" ); document.write( "- and the College of Arts, which has 18 staff, 8 of whom are female.\r
\n" ); document.write( "\n" ); document.write( "Each college has a Dean, who is chosen from the staff in that college.\r
\n" ); document.write( "\n" ); document.write( "a)What is the total number of ways these three Deans can be chosen?
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Algebra.Com's Answer #803517 by ikleyn(52908)\"\" \"About 
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\n" ); document.write( "The University of Ballygobackwards has three colleges:
\n" ); document.write( "- the College of Science, which has 19 staff, 5 of whom are female;
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\n" ); document.write( "- and the College of Arts, which has 18 staff, 8 of whom are female.
\n" ); document.write( "Each college has a Dean, who is chosen from the staff in that college.
\n" ); document.write( "a) What is the total number of ways these three Deans can be chosen?
\n" ); document.write( "b) How many ways can three Deans be chosen, so that at least one of them is female?
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\n" ); document.write( "\n" ); document.write( "            The post contains many words and seems to be a complicated problem,  from the first glance.\r
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document.write( "(a)  For the 1st college, there are 19 choices;\r\n" );
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document.write( "     For the 2nd college, there are  6 choices;\r\n" );
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document.write( "     For the 3rd college, there are 18 choices.\r\n" );
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document.write( "     These choices are independent, since we choose in different / (separate) sets.\r\n" );
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document.write( "     THEREFORE, the total number of triples of the three Deans is the product  19*6*18 = 2052.     ANSWER\r\n" );
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document.write( "         (according to the Fundamental counting principle).\r\n" );
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document.write( "(b) In this part, we should subtract from the total number of cases 2052 of the part (a)\r\n" );
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document.write( "    the number of cases  (19-5)*(6-4)*(18-8) = 13*2*10 = 260, when all the three Deans are men.\r\n" );
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document.write( "    So, the answer is  2052 - 260 = 1792.\r\n" );
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