document.write( "Question 935875: Excluding the jokers, what is the probability of drawing three cards with different mark? The answer is 169/425. Please kindly teach me how to find the answer. Thank you in advance! \n" ); document.write( "

Algebra.Com's Answer #569245 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "We don't understand what you mean by \"different marks\".\r\n" );
document.write( "\r\n" );
document.write( "If you meant three cards like these, different ranks and different suits:\r\n" );
document.write( "\r\n" );
document.write( "J♥, 3♦♦, 8♣,\r\n" );
document.write( "\r\n" );
document.write( "then there are 13C3 ways to choose the 3 ranks, and for each of those ways,\r\n" );
document.write( "there are 4 suits to give the lowest-ranked card, and for each of those ways,\r\n" );
document.write( "there are 3 suits remaining to give the card with the middle-rank, and\r\n" );
document.write( "2 suits remaining to give to the highest-ranked card.\r\n" );
document.write( "\r\n" );
document.write( "The numerator of the probability would be (13C3)(4)(3)(2) = 286*24 = 6864.\r\n" );
document.write( "\r\n" );
document.write( "The denominator would be the number of ways to select any 3 cards, or 52C3,\r\n" );
document.write( "or 22100.\r\n" );
document.write( "\r\n" );
document.write( "That would be a probability of  which reduces to ,\r\n" );
document.write( "not .\r\n" );
document.write( "\r\n" );
document.write( "So we must be misinterpreting what you mean by \"different marks\".\r\n" );
document.write( "\r\n" );
document.write( "Sorry.\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );