document.write( "Question 1178812: 1. From a class of 40 students 8 students will be chosen to join the science field trip. In how many ways can the student be chosen?\r
\n" ); document.write( "\n" ); document.write( "2. In a gathering, the host makes sure that each guests shakes hands with everyone else. If there are 30 guests, how many handshakes will be done? \n" ); document.write( "
Algebra.Com's Answer #808221 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "(1)  In  \"C%5B40%5D%5E8\" ways.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     It is the number of COMBINATIONS of 40 students taken 8 at a time.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     \"C%5B40%5D%5E8\" = \"40%21%2F%288%21%2A32%21%29\" = \"%2840%2A39%2A38%2A37%2A36%2A35%2A34%2A33%29%2F%281%2A2%2A3%2A4%2A5%2A6%2A7%2A8%29\" = 76904685  ways.          ANSWER\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(2)  For a party of n participants, the number of handshakes is  \"C%5Bn%5D%5E2\" = \"%28n%2A%28n-1%29%29%2F2\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     For n= 30 participants, the number of handshakes is  \"%2830%2A29%29%2F2\" = 435.       ANSWER\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "---------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Both problems are on COMBINATIONS.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "On Combinations,  see introductory lessons\r
\n" ); document.write( "\n" ); document.write( "    - Introduction to Combinations\r
\n" ); document.write( "\n" ); document.write( "    - PROOF of the formula on the number of Combinations\r
\n" ); document.write( "\n" ); document.write( "    - Problems on Combinations\r
\n" ); document.write( "\n" ); document.write( "    - OVERVIEW of lessons on Permutations and Combinations\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Also,  you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic  \"Combinatorics: Combinations and permutations\". \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-II
\n" ); document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );