document.write( "Question 1169916: There are 2 Senators from each of 50 states. We wish to make a 3-Senator committee in which no two members are from the same state. How many ways can the 3-Senator committee be formed such that no two Senators are from the same state? \n" ); document.write( "

Algebra.Com's Answer #794762 by ikleyn(52782) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "1-st senator in the committee can be any one of 100 senators, giving 100 options.\r\n" );
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document.write( "2-nd senator can be any one of 98 senators from other states, giving 98 options.\r\n" );
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document.write( "3-rd senator can be any of 96 senators from remaining 48 states, giving 96 options.\r\n" );
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document.write( "In all,  there exists  100*98*96 = 940800  different ways.    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "My note after reading the post by @Math_tutor2020.\r
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document.write( "    @Math_tutor2020 correctly pointed that my number must be divided by 3! = 6:\r\n" );
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document.write( "        940800/6 = 156800.\r\n" );
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document.write( "    I agree with it, in full (!)\r\n" );
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