document.write( "Question 1135369: Triplet X,Y,Z are chosen from the set {1,2,3,.....24,25} such that X grater equal to Y and Y equal to Z.How many such triplets are possible? \n" ); document.write( "

Algebra.Com's Answer #753028 by ikleyn(52786) $\"\"$ $\"About$

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\n" ); document.write( "Since in each triplet (X,Y,Z), the values Y and Z are equal, according to the condition, \r
\n" ); document.write( "\n" ); document.write( "you may forget about triplets and reformulate your problem EQUIVALENTLY in this much simpler way:\r
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document.write( "        Doublets (X,Y) are chosen from the set {1,2,3,.....24,25} such that \r\n" );
document.write( "        X >= Y. How many such doublets are possible?\r\n" );
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document.write( "For Y = 1,  there are  25 such doublets  (1,1), (2,1), (3,1), . . . , (25,1).\r\n" );
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document.write( "For Y = 2,  there are  24 such doublets         (2,2), (3,2), . . . , (25,2).\r\n" );
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document.write( "For Y = 3,  there are  23 such doublets                (3,3), . . . , (25,3).\r\n" );
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document.write( ". . . . . . . .  And so on  . . . . . \r\n" );
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document.write( "Finally, for Y = 25,  there is ONLY ONE such doublet                  (25,25).\r\n" );
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document.write( "So, the answer to your question is the value of the sum  25 + 24 + 23 + . . . + 1.\r\n" );
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document.write( "This value is very well known: it is the sum of the arithmetic progression\r\n" );
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document.write( "    1 + 2 + 3 + . . . + 25 =  = 325.\r\n" );
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document.write( "ANSWER.  The number of such triplets is 325.\r\n" );
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