document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201863>Question 1201863</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many ways can two cars and four trucks be selected from five cars and seven trucks to be tested for a safety inspection? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #836401 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=836401\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Answer: <font color=red size=4>350</font>\r<BR>\n" );
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document.write( "Explanation:\r<BR>\n" );
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document.write( "The order of cars and trucks doesn't matter.<BR>\n" );
document.write( "Use the nCr combination formula.\r<BR>\n" );
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document.write( "n = 5 cars total<BR>\n" );
document.write( "r = 2 cars to pick<BR>\n" );
document.write( "n C r = (n!)/(r!(n-r)!)<BR>\n" );
document.write( "5 C 2 = (5!)/(2!*(5-2)!)<BR>\n" );
document.write( "5 C 2 = (5!)/(2!*3!)<BR>\n" );
document.write( "5 C 2 = (5*4*3!)/(2!*3!)<BR>\n" );
document.write( "5 C 2 = (5*4)/(2!)<BR>\n" );
document.write( "5 C 2 = (5*4)/(2*1)<BR>\n" );
document.write( "5 C 2 = 20/2<BR>\n" );
document.write( "5 C 2 = 10<BR>\n" );
document.write( "There are 10 ways to pick two cars from a candidate pool of five cars total.\r<BR>\n" );
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document.write( "The value 10 can be found in Pascal's Triangle.<BR>\n" );
document.write( "Look at the row that starts with 1,5,...<BR>\n" );
document.write( "We're looking at the third slot because r starts at r = 0<BR>\n" );
document.write( "r = 0 ... 1st slot<BR>\n" );
document.write( "r = 1 ... 2nd slot<BR>\n" );
document.write( "r = 2 ... 3rd slot\r<BR>\n" );
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document.write( "Repeat the previous set of steps to determine that 7C4 = 35, which is the number of ways to pick the four trucks from a pool of seven trucks.<BR>\n" );
document.write( "The value 35 can be found in Pascal's Triangle in the row that starts with 1,7...<BR>\n" );
document.write( "Look in the fifth slot (r = 4 --> 4+1 = 5th slot)\r<BR>\n" );
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document.write( "To recap we found that there are...<ul><li>10 ways to pick the two cars from a pool of five cars.</li><li>35 ways to pick the four trucks from a pool of seven trucks.</li></ul>The order doesn't matter.\r<BR>\n" );
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document.write( "In total there are 10*35 = <font color=red size=4>350</font> ways to pick two cars and four trucks from a pool of five cars and seven trucks. The order doesn't matter.\r<BR>\n" );
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document.write( "nCr calculator<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.calculatorsoup.com/calculators/discretemathematics/combinations.php\">https://www.calculatorsoup.com/calculators/discretemathematics/combinations.php</a><BR>\n" );
document.write( "Pascal's Triangle<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.mathsisfun.com/pascals-triangle.html\">https://www.mathsisfun.com/pascals-triangle.html</a><BR>\n" );
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