document.write( "Question 1112258: In how many ways can a group of 6 people be divided into two unequal groups if there must be at least one person in each group? I've tried combinations formula but it didnt work plz help. \n" ); document.write( "

Algebra.Com's Answer #727272 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "You may have these two basic configurations:\r\n" );
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document.write( "          Table\r\n" );
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document.write( "     1-st group    2-nd group\r\n" );
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document.write( "1    1 persons     5 persons\r\n" );
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document.write( "2    2 persons     4 persons\r\n" );
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document.write( "And, basically, that's all.\r\n" );
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document.write( "Now we need to calculate in how many ways you can collect each configuration.\r\n" );
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document.write( "a)  Configuration #1:  1 person in one group and 5 persons in other group.\r\n" );
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document.write( "    You cam choose one person of 6 by 6 ways.\r\n" );
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document.write( "    In this way, as soon as you fill the first group, the second group is formed AUTOMATICALLY of 5 remained persons.\r\n" );
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document.write( "    So, you have 6 options/opportunities to make the configuration #1.\r\n" );
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document.write( "b)  Configuration #2:  2 persons in one group and 4 persons in other group.\r\n" );
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document.write( "    You can choose two persons of 6 by   =  = 15 ways.\r\n" );
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document.write( "    Working on this configuration, as soon as you fill the first group of 2, the second group of 4 is formed AUTOMATICALLY of 4 remained persons.\r\n" );
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document.write( "    So, you have 15 ways/options/opportunities to make the configuration #2.\r\n" );
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document.write( "c)  Since your options in Case #1  and in Case #2 are independent, you have 6*15 = 90 ways, in all, to make your selections.\r\n" );
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\n" ); document.write( "\n" ); document.write( "-------------------
\n" ); document.write( "On Combinations, see the 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
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\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
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Combinatorics: Combinations and permutations\". \r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r
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\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
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\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
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