document.write( "Question 1168172: Seven prizes are to be given to seven different people in a group of fourteen. In how many ways can a first prize, a second prize, a third prize and four fourth prizes be given? \n" ); document.write( "

Algebra.Com's Answer #851602 by ikleyn(52787) $\"\"$ $\"About$

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\n" ); document.write( "Seven prizes are to be given to seven different people in a group of fourteen.
\n" ); document.write( "In how many ways can a first prize, a second prize, a third prize and four fourth prizes be given?
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document.write( "First three prizes are unique.\r\n" );
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document.write( "First  prize may go to any of 14 participants, giving 14 options.\r\n" );
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document.write( "Second prize may go to any of 13 remaining participants, giving 13 options.\r\n" );
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document.write( "Third  prize may go to any of 12 participants, giving 12 options.\r\n" );
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document.write( "So far, we have  14*13*12 options for the first three prizes.\r\n" );
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document.write( "Next 4 prizes are not unique, and we do not distinct them.  \r\n" );
document.write( "They will go to four different people of remaining 11 people,\r\n" );
document.write( "but the order does not matter, since the prizes of this level are indistinguishable.\r\n" );
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document.write( "So, at this step, we have   =  = 330 different options for these 4 fourth prizes.\r\n" );
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document.write( "In all, all prizes can be distributed in  14*13*12*330 = 720720  distinguishable ways.\r\n" );
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