document.write( "Question 144794: How many ways can 4 people be chosen from a group of 9? Tell wheater the situation is permutation or combination \n" ); document.write( "

Algebra.Com's Answer #105521 by solver91311(24713) $\"\"$ $\"About$

You can put this solution on YOUR website!
It depends. Does the order of the group of 4 people matter? Let's say your group of 9 consists of Alice, Bob, Carly, David, Ernest, Fran, Gillian, Henry, and Iris. Clearly, Alice, Bob, Carly, and David is one set of 4 people that you could select. The question is this: Is Alice, Bob, Carly, and David different from David, Carly, Bob, and Alice? If you were just selecting 4 committee members, then the order doesn't matter, but if you were selecting a Club President, Vice-President, Secretary, and Treasurer, then order would definitely matter.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So, if order matters, then you have a permutation of 9 things taken 4 at a time given by: $\"9%21%2F%289-4%29%21\"$ . Here's a calculation shortcut: $\"9%21%2F%289-4%29%21=9%21%2F5%21=9%2A8%2A7%2A6%2A5%21%2F5%21=9%2A8%2A7%2A6\"$ . \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "If order does not matter, then you have a combination, and the answer you got for the permutation is too large by a factor of the number of ways that you can arrange the group of 4, namely 4!. So you need to divide the permutation calculation by that amount: The combination of 9 things taken 4 at a time is then: $\"9%21%2F%284%21%289-4%29%21%29\"$ . Use the same calculation shortcut from above:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"9%21%2F%284%21%289-4%29%21%29=9%2A8%2A7%2A6%2F%284%2A3%2A2%29=3%2A2%2A7%2A2\"$ . \n" ); document.write( "

\n" );